I stand corrected, but would assert that his observations abd calculations were more direct than that of most people.
I think if you step back far enough to view the motions of the sun and planets relative to the center of the galaxy, you will note that none of the moons or planets travels in a circle (or elipse).
In fact it is the opposite. The Ptolemaic theory is very direct and the Copernican theory (which Galileo supported) was substantially more subtle (but also much better of course). The former assumed a central fact - the earth is not moving - based on direct sensory evidence. The motion of the sun, moon and planets is also directly apparent. So the the theory applied the simplest possible motion to them, this is pretty darn direct. When deviation from observation was found, they added another layer but this is also direct. More deviations found, add another lay on top. It is brute force programming.
In contrast, Copernicus begins by denying the obvious fact that the earth is not moving. I don't recall that he or Galileo had an explanation for how the earth could be moving but we not feel it.
It is interesting that, about the same time as Galileo, Tycho simplified the Ptolemaic scheme by having the sun and moon revolve around the earth but the planets revolve around the sun. At the limit of observational capability of the time, I don't think Tycho's scheme could have been distinguished from Copernicus' which also used circular orbits. Even a Keplerian system with elliptical orbits cannot be distinguished from a Tychonian system that does also. I think the reason the geocentric view lost out is that it cannot account for the seasons unless the earth's axis moves. Once you let the earth move, why not go all the way for the simpler (but more subtle) scheme?