Antikythera mechanism, etc.
It’s not so far-fetched. After all, the Greeks learned writing from the Phoenicians, so why couldn’t they have picked up an astronomical calender from the Babylonians? I’m referring to the time line, not the device itself. Few cultures exist in isolation, and the Greeks certainly did not.
It makes sense that people who were good at mechanics, and who also studied astronomy, would try to mechanically replicate the motions on the planets, sun, and moon. The Greeks and Babylonians probably tried out all kinds of gearing. The more accurate the results the more likely the device would be reproduced and put into use. The internal workings of an accurate device would be pleasing to those involved in either field. And it seems likely that astronomical theories would be influenced by any really good mechanical device.
Astronomy, mechanics, and calendars are all tied in together - an area of fascination to me.