I can't answer for all pre-Galileo cultures, but in the Greco-Roman world, at least, from the 4th century BCE onwards experts had at least as good an understanding of the nature of the sun, earth, and moon as many modern laypeople.

In terms of specifics, they were off on the absolute sizes and distances of the sun and moon, and the lack of any understanding of gravity meant that a heliocentric model was not at all obvious, but in terms of relative sizes they weren't too awful. The moon was understood as a spherical rocky body, like the earth. They often had the same idea of the sun, which is why Lucian has people living on the sun too. That possibly sounds more wrong, but they at least had the right idea that the sun's light and heat aren't caused by fire but by glowing in the same way that a hot rock or hot metal does (which is accurate, apart from the sun not being nearly as dense as rock; nowadays we call it black-body radiation).

That hadn't always been the case. Anaximandros (or Anaximander), in the 6th century BCE, had believed the sun and moon were openings into a hot region of the cosmos called the aithēr; and a near-contemporary, Herakleitos (or Heracleitus) believed they were bowls of fire, which occasionally turned around to cause eclipses. The idea that the moon was a solid body that received its light from the sun was first proposed by Thales, another contemporary, but in Thales' time that was just guesswork; it wasn't universally accepted until around the time of Empedokles and Plato (late 5th, early 4th century BCE). In the 5th century Anaxagoras taught that it had hills and valleys, like the earth. Here's some more details in an older post.