Steam engines and other technologies simply had no hope of happening on a large scale until materials science, including metallurgy and chemistry, had caught up, and that wasn't going to happen for a very long time regardless.
Newcomen steam engines did not depend on any metallurgy, chemistry or material science the Romans didn't have. These are low pressure steam engines; the work is done by atmospheric pressure when the steam is condensed. They can be built with a copper boiler and a hand-finished cast brass cylinder with leather piston seals.
The Romans could do all of this, but nobody had the idea. And it's the sort of idea that doesn't just spring into somebody's head out of the blue, Newcomen was applying principles and ideas other people came up with first (story of the entire industrial revolution.)
