@Roboramma
Well, we're going off target for this thread topic, but personally I tend to favour Richard Carrier's case for it. My simplified and adapted version goes kinda like this:
- what made an industrial revolution even possible was a massive increase in energy per person employed in that. Far more than water and wind mills could provide,
- the steam engine provided that,
- early steam engines sucked hairy ass (not his exact words

), compared to other sources of energy,
- but eventually England's massive shipbuilding created a shortage of wood for, say, charcoal and created a massive market for mined coal. It wasn't an ideal source (see why we STILL need coking plants to sort coal from rocks, and convert coal into something as good as charcoal), but that still was cheaper, so hey,
- eventually they mined below the ground water level, and started to need to SOMEHOW pump that water out to keep mining coal, and
- steam engines were a convenient way to pump water out. Like, you wouldn't even need much infrastructure or supply lines or anything, you could just take some of that mined coal, put it into the engine that allowed you to mine more coal.
- eventually, steam engines would get a lot more powerful and useful, but they basically needed to be subsidized by the coal mine owners to get past that hurdle.
- but the conditions for that initial need for steam engines, just weren't there during Ancient Rome, or really, at any point before the 18'th century or so.