But we do all run on steam

All (non-renewable) power plants are steam driven. Even nuclear power is a glorified steam engine. What we don't do so much any more is drive directly using the steam, it's now a stage removed from the effect. The steam drives the turbines to generate electricity that drives your machines. As soon as you swap to an electric car, that will run primarily on steam (until wind/solar takes over).

We streamlined it, we hid the pipes and the smoke, toned down the brass and the grease, but it's still all steam powered.

Antoine Lavoisier should not have been executed

Lavoisier's importance to science was expressed by Lagrange who
lamented the beheading by saying: "Il ne leur a fallu qu’un moment
pour faire tomber cette tête, et cent années peut-être ne suffiront
pas pour en reproduire une semblable." ("It took them only an instant
to cut off this head, and one hundred years might not suffice to
reproduce its like.")

While Lavoisier is known as one of the greatest scientists of his time, he was also a philanthropist and, more importantly, a competent administrator. Before the Revolution, he had been the manager of the Gunpowder Commission, and an excellent one at that. Anecdotally, he appears to have been of a great help to the founder of the DuPont company.

Alas, he was basically framed for the terrible fiscal and domestic policies of the government under the Terror, which made him a convenient scapegoat and gave a pretext for confiscating his fortune. He was summarily convicted with ballooned charges and executed.

And yes, I am still bitter about it.

Now, had he survived the Terror and made it to the quite scientist- and engineer-friendly Napoleonic regime, you can have him develop technologies early. The obvious ones are high-grade steel (that is, more modern blast furnaces) for high-pressure steam engine, smokeless powder/solid rocket propellant and rocketry, or let's be crazy pulsejets and later even maybe ramjets. He had already invented a way to produce hydrogen, and hydrogen balloons were becoming a thing, and he may further pursue the idea as well.

Avoid anything having to do with electricity, though - you want those technologies not developed early for steampunk to work. Ideally, you want them to take a backseat because other early tech are prioritized. So you can have rocket/ramjet supersonic planes without electricity, if you want.

Time travel is a bit harder to place on the tech tree, so you will have to use some handwave there.

A side-effect may be, even with a small technological edge, that Napoleon ultimately wins, or at least ends up with enough strength to impose an advantageous status quo. The Indian subcontinent will be very happy, Spain not so much. Geopolitical consequences are beyond the scope of the question, but at least this would change from the ubiquitous Steampunk British Empire.

You can't do it.

The reason that technology doesn't exist is because the world just doesn't work like that - we just didn't know that during Jules Verne's time.

Change the timeline as much as you like, the laws of the universe don't change.

Vhs or Betamax? QWERTY or Dvorak? MP3 or WAV? HTML or some long-forgotten alternative? Should we drive on the left or right side of the road? How wide should train tracks be?

All of these are example of cases where two possible ideas came along at or near to the same time. Some people made one choice, others the opposite choice. For the first four examples, one of the two arrived just enough earlier, or had better advertising, or was able to saturate the market faster, or some other small factor, as to become the "better" standard in the eyes of the buying public, and therefore killed off the competitor. In some cases, one can argue the losing choice carries clear advantages, but not enough to overcome the tidal wave of momentum gained by the ultimate winner.

This is all you need. An inventor with right gumption and determination, coupled with charisma, foresight, and so on, who gets steam ready at just the right time, gets it in the eyes and hearts of the public quicker, and makes it essential to life as they knew it. Now, gasoline and electric can come along and tout itself to the stars, but people won't care- they already have that machine in a steam version, which is cheaper, easier to find parts and service, and works just fine, thank you.

Come to think of it, this is exactly the situation electric cars are having right now. The infrastructure around gasoline is everywhere, and is comparatively cheap. They probably will make it, but they will struggle as they have been for several more years before they do.

What if Nikola Telsa had prevailed and Edison had not?

Telsa had promised the transmission of electrical power without wires. If this technology had not succeeded (perhaps Marconni's radio interfered with it's success? Or electricity itself was deemed to be too dangerous.) Then Telsa could have improved upon his orginal idea of a steam oscillating generator to supply local power where needed. Or perhaps he could colaborate with Madame Curie on to the possiblity of a small nuclear powered steam engine powering everything directly and electric powered devices would have stagnated.

Everyday people would just refer to these power plants as ‘dynamos’. Steam power could be transfered around the house by a series of leather belts, steam pipes or, in some cases, pistons. Most of the gadgets we use in modern life (other than personal electronic devices) could be powered by dynamos the size of a small furnace. Office machines, bench mounted tools and household appliances would operate as normal. They would just have to be grouped close together to conserve the kinetic energy or super-heated steam.

Imagine a steam-powered CERN super collider. Another source of motion is pneumatic tubes. If you can generate a strong enough vacuum you can move surprising amounts of weight. There was even a proposed subway system that was to be powered by clean efficient giant pneumatic vacuum tubes.

Basically you would have to supress electricity and greatly increase the efficiency of steam as a power source to create a truly steampunk world.

Fashion, and little else

Let's look at the late 1890s to early 1900s.

Airships existed. They were powered by internal combustion engines, but lightweight (relatively!) steam engines existed which would have worked.

Internal combustion engines were taking over on cars, but steam cars still existed. (Fun fact - you could wheelie them.) Heavier transport - trucks and tractors - still used steam. And ships and railways still used steam and coal.

Electricity existed, but was not widespread. Lighting and heating was still mostly gas.

So what's technically different from steampunk? Simply the aesthetics. If someone could have made that look fashionable, in the same way that military-style outfits went through phases, then you'd have the whole package.

Of course not time machines or airships to the moon, but then we do still have the laws of physics.

A steampunk world only has Victorian science, but some people have lots more money to spend on ornate brass machines. Why would science have stopped? If any one country stopped research, others would quickly over-take it and the knowledge would spread anyway. Therefore I think that means that one state (obviously the British Empire ;-) must be running the whole world. Without competition and the threat of a scientifically advanced enemy, there's no need to invest in science research. Research might even be banned to make it harder for the masses to revolt.

In such a state, there would be a fabulously wealthy elite who demand unnecessary ornamentation to show off their status, and vast numbers of semi-slave people to build the machines and shine the brass.

So, no new physics but probably a powerful secret police to maintain the status-quo.

A series of major solar storms like the Solar Storm of 1859 hitting planet Earth just in time when the first electric networks were built.

Mankind decides that major electric networks are unreliable and a network of pipelines for oil, gas, steam, and warm water is established as the major means of power distribution. Energy is locally converted to power, light, or whatever is needed.

This world will have a lot of steam punk technology in it.

This technology is less efficient than the electricity based technology we have now, but given the circumstances considered more reliable.

EDIT: I just noticed the requirement that a time traveller should be able to arrange for the critical event—I have no idea other than handwaving it, a technology to control solar flares is far out of our current reach.

If combustion engine never happened, oil would mostly be worthless black sludge and personal automobiles would never have become every mans accessory equally fast if at all.

But if electricity still was developed then maybe we would have had electric rails in cities. Like trams and subways without steam inside cities. Steam trains between cities. Most power plants would still work as they still rely on steam or wind or water driving a turbine generating electricity. Even solar can be done this way, although probably very inefficient compared to geothermal alternatives. But it would be good enough for electrical lighting for everyone. Maybe not electrical cooking and heating..

It is difficult to say if automobilism would ever happen. Oil was the thing which made this revolution possible. Battery technology is still not quite there for electric driven automobiles today, ~150 years later. If airplanes were possible it would most likely be propeller driven planes. Jet engine we can forget if we don't have combustion engine.

Mostly it's a logistics problem. Most stereotypical steampunk stuff would be extremely inefficient and costly to produce and use. Think back to the Edison/Tesla situation: Edison wanted power plants on every block to produce power, while Tesla argued that central distribution plants with efficient distribution methods were better. Tesla won out because he was right about how important efficiency is to mass adoption.

Steampunk has the same problem: things powered by steam have to convert fuel into energy indirectly using the conversion of water to steam, as compared to electricity or internal combustion engines where the energy from the power source can be applied far more directly, with less big machinery. Steam engines tend to be big and inefficient and require a lot of fuel compared to devices powered by an electrical grid or directly by petroleum internal combustion. That fuel and the metal needed to produce them also makes them heavy and expensive as compared to more "modern" designs based on plastic, aluminum and electricity. Most steampunk concept art I've ever seen has always shown big, ornate machines made of iron and brass, with lots of wasted materials: the devices we tend to imagine as "steampunk" would be large, temperamental, heavy and expensive. A steam-powered airship to the moon would be prohibitively impractical because the amount of fuel needed to move an iron-and-brass monstrosity capable of withstanding vacuum conditions would be impossible to produce economically (especially since you'd also have to move all that fuel along with it).

Bottom line, steampunk isn't economically viable or physically practical for large-scale use, especially compared to more practical technologies we've developed since the days of the steam engine. If you want to make steampunk make sense, you'd have to create fictional resources to make such inefficient technology workable (things like the Ghost Rock super coal from Savage Worlds: Deadlands and the super-strong-and-light Rearden Metal from Atlas Shrugged), and you'd have to prevent things like electricity, petrol, plastic and high-strength alloys from ever being effectively developed.

Side note: you could argue that aluminum could be used to create stronger, lighter steampunk devices, but aluminum isn't really something that comes to mind when thinking of steampunk, and since aluminum wasn't really commercially viable until the very late 1800's, it might not make sense to use it for 19th century technology anyway. That would be up to you, but a story with aluminum steampunk gadgets would feel odd in my opinion. You could also argue that Rearden Metal is just a high-strength alloy, but since its composition and production process are never really explained, it has a mysterious, alchemical sort of feel that would work nicely in a steampunk story. Alloys based on real-world technology would stick out oddly in readers' minds in a steampunky, mad-science sort of story: if they can invent titanium alloy, why don't they have plastic yet? You could make it work, but you'll start to get into the only-this-and-not-that sort of game that makes readers think you're cherrypicking to make an illogical plot work.

The Death of the Young John D. Rockefeller

The only resource/technology that displaced coal as the major energy source, and thus "changed" history, was petroleum. While it is true that most electricity comes from coal today, it is also true that petroleum revolutionized transportation. Without oil, there would be no aeronautic and automotive industries (as we know them), and navigation would be way slower. Commerce and war, among many other human activities, would be very different. Oil shaped the world, and more to the point, prevented coal technology from evolving further.

A few examples will suffice to prove the point:

1. World War I was the first fully mechanized war, with tanks, airplanes, cars and motorcycles playing a major role. In the sea, the UK had to switch from a coal-fueled fleet to gasoline in order to compete against the faster German fleet, even though there were important coal reserves in Great Britain but no oil at all (at the time). War would never be the same.


2. Urban planning in the US was centered on gasoline: highways, suburbs, shopping malls, etc. were designed so that every American would need a car. Oil demand met the oil supply and the oil industry became a key pillar in the economic expansion of the US.

From this angle, one historical event that had to change to make steam technology possible would be the development of the oil industry.

Despite its importance today, in the nineteenth century, oil was not considered an energy source at all! It was extracted to produce kerosene, a dirty substitute for sperm whale (cachalot) oil which was the finest illuminant available. Sperm whales were hunted near extinction and merchants started looking for substitutes coming from plants, coal and a disgusting dense liquid known as petroleum or oil rock.

John D. Rockefeller made its fortune by selling refined oil that met a standard composition suitable to be used in kerosene lamps without exploding or other life-threatening hazards (hence the name of his company, Standard Oil). He was a key figure in the development of the oil industry from a wild and unstable activity, subject to "oil fevers" that attracted fortune seekers, to an organized venture that integrated the whole production process, from geological exploration overseas to gasoline stations.

So one possibility is that, in the original timeline, Rockefeller dies in an accident in his refinery, coal-based electricity becomes widely available and the oil industry does not unfold further from a dubious venture restricted to sporadic, local bonanzas before falling into oblivion.

The Universal Physics Translation Event of 1804, which never happened, needs to have happened, for much of that to be feasible and economical.

Otherwise:

Minor bits of Everything in the Big Bang, or possibly before.

On a smaller scale, maybe have the evolution of life on Earth take a different path, one that produces beings that can achieve some of that via different means: being more receptive to brass implants; capable of precise crafting by feeling and generating exact vibrations via decent tools; think in more dimensions like Dr Manhattan from The Watchmen; make (to us) implausible designs work by the power of sufficiently concentrated belief, à la the Ork Waaagh! from WH40k

But that would make all of those feats as mundane as staying solid is to us.

"Steampunk" covers a great lot of little things that are not possible even now. It's essentially magic.
You may get better answers if you asked about a single specific accomplishment, instead.