Considering how fragmented the pre-modern historical record is and how little attention is paid to technology in most of the sources we do have, it's quite possible that someone did build a Newcomen style engine 2000 years ago, it could even have happened many times.
However, it was probably only worth using one once labor costs reached a certain threshold. e.g. if you were an ancient roman landlord with abundant slave labor, why would you go to the trouble and expense of building steam engines to remove water from your mines rather than just having some workers work the pumps?
Moreover a Newcomen engine was so inefficient that it was really only usable when sited right at a coal mine, and in ancient times there were plenty of surface coal sites that didn't require deep mines (and thus pumps).
It's hard to imagine someone leaping straight to a Watt engine, especially given the metallurgy required.
However, it was probably only worth using one once labor costs reached a certain threshold. e.g. if you were an ancient roman landlord with abundant slave labor, why would you go to the trouble and expense of building steam engines to remove water from your mines rather than just having some workers work the pumps?
Moreover a Newcomen engine was so inefficient that it was really only usable when sited right at a coal mine, and in ancient times there were plenty of surface coal sites that didn't require deep mines (and thus pumps).
It's hard to imagine someone leaping straight to a Watt engine, especially given the metallurgy required.