Technological revolutions aren't just driven by opportunity, but also practical need; mine draining was the first "killer app" for steam that let it catch on because it solved a real problem and allowed it to be proven as a concept.
But England was also in a unique position in other ways: It had natural resources like coal and iron, as well as rivers to efficiently transport these, a stable government, and relatively high wages compared to mainland Europe, which served as an incentive to replace workers (and animals) with machines. All of these stars aligned at the right time for steam to become a viable entrepreneurial project, which simply wasn't the case in, say, Germany or France.
1: https://solar.lowtechmagazine.com/2011/12/how-to-downsize-a-...
Many inventions are like this. They seem simple in hindsight, but at the time, required putting together tools, techniques, materials and insight from multiple sources. There's an old BBC TV show called "Connections" that explores the origins of many modern technology and the often strange paths that led us there. For example, without people loving perfume, internal combustion engines might have taken decades longer to have been developed.
Kind of like how some countries in Africa skipped landlines and went straight to mobile phones, I can let the Romans stumble onto just the right ink recipe a bit early.
I've always found it fascinating with the history of the Industrial Revolution that it wasn't so much about technology, as about the exact right circumstances arising so that the technology could be used and improved. There had to be industrialists, an industry that needed the invention badly enough and people rich enough to be able to gamble on the unproven inventions. The technology itself (as others have said) rests on the shoulders of multiple layers of giants. The society had to be willing to change, and cope with the new inventions and their social consequences (Britain nearly wasn't, as the Luddites showed, and both China and Japan sealed themselves off from foreign inventions to preserve their societies unchanged).
From what I know of late Roman society, it was stratified and fixed, an oligarchy. Any threat to the patrician class would not have been accepted, and the patrician class had no reason to change. This is different from 18th Century Britain where the rising merchant class were challenging the remnants of the feudal peerage, who didn't have enough power to stop them.
I think your premise is interesting, but only as fiction.
The Industrial Revolution changed British society, moving power from the feudal aristocracy to the new merchant class. It could only happen in a time where the feudal aristocracy were weakened (this is relatively shortly after the English Civil War). And also when the working class was not so powerful - the Luddites also resented the changes created in British society.
I think you could work with this, though - have the Forum discussing the changes, some backstabbing and politics about who gets licenses to use the new technology, who profits from it, who gets their traditional livelihoods destroyed. And introduce the Roman version of the Luddites - peasants deprived of their ancestral livelihoods by the new technologies.
'Recruit a bunch of people to study rocks. Use acid and scratch tests to figure out which ones can be smelted for valuable elements. Recruit a bunch of people to study making alloys. Form an R&D team to develop precision lathes. Invent index cards and file catalogs.'
Before the Saxony (flyer) spinning wheel was developed and spread through Europe in the late Middle Ages, about 9-10 spinners using hand spindles were required to keep one weaver in sufficient yarn (thread), and that includes the most tedious part of weaving, dressing the loom. Such was the need for yarn that most girls and women spun hours a day - possible while waiting for something to cook, watching children, walking around the village (I was able to spin while walking within a few weeks of learning)
Even with spinning wheels, there were still more people spinning than weaving. There were advances in loom technology in the early 1700s that increased the spinner to weaver ratio again. It wasn’t until Arkwright’s Water Frame that a powered device could reliably spin yarns strong enough to be warp; the Spinning Jenny that preceded it produced less-strong yarns.
Anyhow, ACOUP has a really great textiles series that shows some of that math. TL;DR - it’s all about the spinning (and the picking and combing)