What are you expecting entering this topic? I don't know. Either way, let me explain.
Heliocentrism isn't wrong, but inefficient: In that case, both the moon and the sun will orbit around the earth, while planets such as Jupiter and Saturn, with themselves many moons around them, are calculated to orbit a center that is closer to the sun than the earth. This would mean to calculate about Ganymede, you first have to calculate about the Sun's motion, then the motion of Jupiter, then Io. That is super inefficient. Instead of that, why don't we set the reference at the Sun?
It is the old religious who fixed the reference at Earth and accepted nothing else, not Galileo nor Copernicus. Galileo, Copernicus, Kepler, etc... just provided new references that made calculation and observation more efficient.
In reality, we technically can define the Earth's surface as flat and anything tangential to the Earth "above it". The problem becomes that if some object flys directly above the south pole, the position for that object on the "flat earth model" would teleport from one side to another. All constellations would be on one side of "earth", the other side being what is "underneath the Earth", which we will have a mantle and core as wide as the surface of Earth itself. We can just fold space enough so that the Earth's curvature matches the morphed space so the Earth is flat according to that system. In that case, the earth is flat.
Due to astronomical, geological, geographical(continents in the South will be disproportionally enlarged), physical, and maybe even archaelogical inconvenience, we pretty much discard this model the moment it is being formed in one's mind. That is why this model wasn't being thought of before with great depths, hmm, I guess.