And particular, the metal working lathe, which wasn't invented until 1700s. A proper steam engine that actually performs useful work better than just having a dude stand there and move whatever you're trying to move requires very tight tolerances around the cylinders that were previously unobtainable.

It is still an interesting question. How can a society that created a 52-pipe musical organ in 228 BC fail to create, even by accident, high-leverage machinery like the steam engine? It reminds me of the Egyptians, who knew of the wheel but apparently only used it in toys.

https://en.wikipedia.org/wiki/Water_organ

I'm not sure if we're taking about different time periods, but weren't they at the forefront of chariot warfare during the bronze age?

And I vaguely recall that inventing bellows to melt iron took a long time too, so steam machinery seems pretty far off if all you have is bronze and stone.

There are reliefs of Ramses II fighting on a chariot and he's from the 1200-1300 BC, so the wheel must have been used much earlier than that by Egyptians.

The Egyptians had chariots, they definitely used wheels.

sort of. they had Aeolipile which is a primitive steam engine but it was looked at as more a curiosity than as a practical tool.

I was thinking about this, what really started the industrial revolution? I think the aeolipile, like other contraptions was just seen as a toy. Could it be that the Newcomen engine proved that real value and work could be done using machines in this way? Maybe just knowing that it was possible after being demonstrated by the Newcomen engine really kicked it off rather than some nebulous societal conditions.

Newcomen solved a real problem and created a virtuous loop: it helped pump water from coal mines, which made coal cheaper to extract, which helped keep the (quite inefficient) machine running long enough that it could be refined to the point that it could be used elsewhere.