Question

What did Sophists think of cosmology?

Answer 1

Doesn't really matter as they were pretty much wrong! They did make contributions to rational thinking more broadly.

Explanation:

The Sophists were a pre-scientific approach to philosophy that, in terms of origin of the Earth and "heavenly bodies" were very big on "air connected theories". See example:

Diogenes the Apolloniate premises that air is the element, and that all things are in motion and the worlds innumerable. He gives this account of cosmogony: the whole was in motion, and became rare is some places and dense in others; where the dense ran together centripetally it made the earth, and so the rest by the same method, while the lightest parts took the upper position and produce the sun. (Kirk, Raven, and Schofield: 1983, 445)

http://www.iep.utm.edu/diogen-a/#H5

We now know that this idea was almost completely wrong, except maybe the importance of air on Earth.

More broadly, the Sophists did contribute to the broader skills of thinking logically and rationally about issues. However, like most Greek "arm chair" philosophers, they didn't see the need to actually go out in the world, make observations and then form ideas - the scientific approach. This had to wait for another 1600 years or so for the scientific revolution to take place.