No. Babylonian astronomers created arithmetical techniques for predicting key events of the moon and planets, such as the date that Jupiter reached a stationary point in the sky. (The stationary point is the positions where Jupiter starts its retrograde motion). They were not trying to explain the nature of the universe (cosmology). Ptolemy derived cosmological models based on geometry, but even he was interested in prediction, not explanation. In both cases, it does not matter whether the astronomer's view is helio- or geo- centric. Ptolemy used a geocentric model, but he did point out that a heliocentric version was a possible alternative.

Even Copernicus was not really that concerned with cosmology: he was showing an alternative to Ptolemy based on the heliocentric view of what he thought was the universe (now known to be the solar system).

In my view it was Galileo who really first proposed that these models went beyond prediction to describe the reality of the cosmos.