huh. Who thought it was a god?
The whole idea opf what exactly constitutes a God in ancient thopught is pretty convoluted and tends to give modern theologians raised on very different assumptions headaches.
But that said - Hellenistic science was pretty advanced, and both experimentation and speculation were encouraged. The latter was more respectable to many philosophers, but there were many people who would have readily agreed with the Galilean idea that 'God speaks maths'. Their maths were a bit more cumbersome than Galileo's, which is part of the problem.
The heliocentric view was advocated variously and accepted widely, but no proof of it could be provided as far as we know (if it was, it saw no wide currency, curse of a non-printing society). Thus, the opposed idea was eventually to enter European tradition through Ptolemy, who, whatever his faults were, constructed a pretty bloody impressive and coherent mathematical system around it. If anything like it existed for heliocentrism, we don't have it, and we oughtn't forget that after Copernicus it took the best astronomers of Europe several generations to come up with a heliocentric model that worked as well as Ptolemy's.
So, let's assume Ptolemy assume heliocentrism. There is the off chance that his model will not be accepted because it is considered 'pagan' (putting Sol Invictus in the centre?), but it may equally well be embraced. No big difference, I would say. Except that it would breakl the pattern - European tradition has a record of picking the poorest models from Antiquity, right down to Cosmas Indicopleustes (they had Strabo, the Periplous and uncounted lost records, but they made the effing Christian Topography the standard work...)
Now, a survival of the scientific method as practised in Hellenistic times would be a completely different thing, but that would need bigger changes upstream. A heliocentric model alone is still likely to be challenged once systematic observations and advanced mathematics make it clear that epicycles don't work.