This kind of fiction is pretty popular in Russia. So there are websites and forums that discuss the kind of hand-waving needed to make the stories interesting (I recommend https://www.popadancev.net/ ).
And one thing that really stands out is that there are really not that many shortcuts. To build something like a steam engine, you need to invent advanced steelmaking, casting, advanced tooling (lathes, drills, etc.), and so on.
In general, ancient people were able to exploit the tech available to them with great efficiency.
There are some technologies that were overlooked longer than they should have, but not that many. For example, rubber could have been invented 400 years earlier. Hooke had a microscope capable of resolving micro-organisms in 1665, but the germ theory of diseases took 300 more years to develop.
I actually disagree a bit. The whole premise of the story is that there are shortcuts indeed, when someone has the entire tech tree available at the push of a button.
The Romans were very capable engineers. If you give them a few key ideas and steer them away from dead ends, progress can compress a lot.
But the economics don't work. A bronze steam engine would have been extremely expensive and it would have taken multiple attempts to work out the best alloy mix. Without refinement the result would have had a low power output and short working life.
Even if you have a blueprint, a bronze engine is still a major research project.
The economics don't work only when compared to the modern alternative. The economics of a grindstone attached to a waterwheel don't work today but they did historically. A steam engine with low power output could still have been extremely useful in the right context despite not being up to the more strenuous tasks of historical variants.
Two things:
1) This idea has been debunked...a lot. The Romans were capable but they were nowhere near an industrial revolution
2) Necessity is the mother of invention. The Romans didn't really need an industrial revolution, or at least their power base didn't.
This is do-able, because it doesn't require much metalworking. This is technology from 1700-1750 or so, made from wood with a few metal bits. Roman technology was capable of that.
Dude, wtf are you talking about? 1750 is freaking high-tech. They had large scale iron casting, gunpowder production, precision engineering good enough to make a clock that can provide accurate time after going around the world, most of the modern math foundations, telescopes, and even steam power.
Clockmaking goes way back, but for a long time was off in its own technological niche. People with tiny files working brass made clocks by hand. The first mass produced clocks appeared in the late 1700s.
Precision didn't come to iron and steel until Maudsley's lathe, around 1800. It can be seen at the Science Museum, London. It looks like a modern lathe, but is quite different from its predecessors. It's on display, but not emphasized, and few people know its importance.
Today we think of engineering as a continuum, where you pull the technology you need from mechanics, electronics, materials science, and chemical engineering to get something done. That's a modern concept. For most of history, those groups barely talked. For a long time, there was a huge distance between science and engineering. Science was sort of an aristocratic hobby, and engineering was done by people who worked in forges and shops. It wasn't until the era of the steam engine that both sides started talking much. They had to figure out thermodynamics to get steam engines to work efficiently.
You certainly can avoid a lot of dead ends, but we're still talking about the span of at the very least multiple decades.
And the next question is practicality. You can make a steam engine demonstrator from bronze. But bronze was expensive, and of varying quality. So your engine will necessarily be low-power, and too inefficient for practical use.
It should have been possible to create electricity with waterwheels. You ”only” need copper.