The most complex machine of the Roman era was perhaps a water organ. (I would guess that for long historical periods the most complex machines were keyboard-controlled musical instruments.)
I'll start: https://en.wikipedia.org/wiki/Aeolipile
... what other things / proceses / materials / frame of mind made the steam engine possible vs. this.
What made for an industrial revolution in the 1800's vs. the 1st century AD).-