The only reason the Romans could not have invented the steam engine was that the Greeks already did before them:

https://en.m.wikipedia.org/wiki/Aeolipile

They had a Lathe too.

I didn't know the Romans had the lathe. Thanks for the correction.

But they did not have a metal lathe, which is substantially more sophisticated. Invention of the metal lathe is credited to Henry Maudslay around 1800.

While steam engines with pistons existed before, the poor sealing because of inaccurate bores and pistons, made them not very efficient.

Incredible. I found this video that shows how the Aelopile works: https://www.youtube.com/shorts/trUtLLu_Ono

What an awesome invention!!!