Bret C. Devereaux's wrote a very interesting article on this topic in his blog. See: https://acoup.blog/2022/08/26/collections-why-no-roman-indus...

His central observation is that the Industrial Revolution involves "coal, steam engines, textile manufacture and above all the harnessing of a new source of energy in the economy", but that "each innovation in the chain required not merely the discovery of the principle, but also the design and an economically viable use-case to all line up in order to have impact."

Thomas Newcomen’s atmospheric steam engine from 1712 were so inefficient that it made only economic sense in circumstances where energy source is very, very cheap. That was inside of coal mines (not in any other kind of mine), because there coal was cheapest. So the Industrial Revolution required as a starting point that all other kinds of energy sources were so expensive that coal mines made sense, and not any kind of coal mines, but deep coal mines that required a lot of effort to pump water out of them. In other kinds of mines horses would have been cheaper than an atmospheric steam engine. In other words, intensive coal mining had to come first and then the Industrial Revolution followed, not the other way round.

It took over half a century, until 1776, that the steam engine in James Watt's desing had been improved so much that its use made economic sense outside of coal mines, namely in the textile industry. It was in the 1700s that looms and especially spinning machines had improved so much that their combination with Watt's steam engine made sense.

Then there was the combination of steam engines with new methods for drilling cannons. The cylinders needed for steam engines used technologies that had been improved over a long period of time in gun production. Then the steam engine itself was combined with the new invention of drilling cannon barrels (instead of casting them). This resulted in better cannons and also helped to further improve the cylinders for the steam engines.

So why not the Romans? -- Devereaux writes:

"_none_ of these precursors were in place. The Romans made some use of mineral coal as a heating element or fuel, but it was decidedly secondary to their use of wood and where necessary charcoal. The Romans used rotational energy via watermills to mill grain, but not to spin thread. Even if they had the spinning wheel (and they didn’t; they’re still spinning with drop spindles), the standard Mediterranean period loom, the warp-weighted loom, was roughly an order of magnitude less efficient than the flying shuttle loom, so the Roman economy couldn’t have handled all of the thread the spinning wheel could produce."

"And of course the Romans had put functionally no effort into figuring out how to make efficient pressure-cylinders, because they had absolutely no use for them. Remember that by the time Newcomen is designing his steam engine, the kings and parliaments of Europe have been effectively obsessed with who could build the best pressure-cylinder (and then plug it at one end, making a cannon) for three centuries because success in war depended in part on having the best cannon. If you had given the Romans the designs for a Newcomen steam engine, they couldn’t have built it without developing whole new technologies for the purpose (or casting every part in bronze, which introduces its own problems) and then wouldn’t have had any profitable use to put it to."

"All of which is why simple graphs of things like ‘global historical GDP’ can be a bit deceptive: there’s a lot of particularity beneath the basic statistics of production because technologies are contingent and path dependent."