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Not quite. Heliocentrism was introduced around 270 BC by a Greek astronomer.

The oldest estimates for the Antikythera Mechanism are 205 BC.

So it is very well possible, if not likely, that the builders of the Antikythera Mechanism were aware of the heliocentric model.

Amazing. Also amazing to me is the caluclation of the size of the moon and distance of the earth from the sun around the same time [1] [2]

They might have been "aware" of it the way people were aware of Evolution before Charles Darwin.

Even Erasmus Darwin (Charles Darwin's grandfather) discussed evolution but Charles really filled in the gaps.

So it might have been an early developing model with discussion among contemporaries before it really "landed".