I've read somewhere how the English people industrialized because they had problems that could not be fixed by human or animal power. Mines became too deep, pumping too hard. The ancient greek knew about steam engines, but had no use for them. The English did, in their mines. Necessity as mother of invention. Then machines freed us from hard labour and gave us free time.
This perfectly demonstrates the point: Before James Watt came along, neither had the English. Steam was unreliable, broke down a lot, killed people, and was only tolerated because it was the only game in town. This bothered society, so money became available so smart people could sit down and give it a solid theoretical basis.
The greek had plenty of smart people, but nobody bothered to assign them the unreliable steam problem. There are secondary problems like metallurgy, but smart people can work on them or find away around them, too.
England started experimenting with steam because it _could_. Newcomen's atmospheric engine required metalworking that was flat-out impossible before the advent of modern(ish) iron-making processes.
Greeks would have needed to perfect large-scale iron-making. And in England's case, it was itself driven by the need to manufacture things like cannons, anchors, chains, etc.
If you somehow got transported into Greece with a perfect knowledge of steam engines, you first would need to spend several lifetimes researching the iron metallurgy. You would be able to build a toy steam engine out of bronze, maybe, but good quality bulk bronze was expensive enough to be used as currency.
