Heliocentrism didn't come about just from observing the sun. We also had to observe the planets and figure out why they would suddenly change direction in the sky. After centuries of increasingly complex models that decently described the planetary motion with geocentrism, some calculating and new models that put the sun at the center made a lot of the models much more consistent.
Exactly. It's not that a geocentric model can't be mathematically described and used to predict, it's just that the math is much, much easier if you put the sun in the middle.