At the time, optical theory was not advanced enough to explain how telescopes worked. So Galileo had to trust on faith that his instruments were measuring what he thought they were measuring. It’s not scientific, but Galileo was supported by a consensus of astronomers, including Jesuits.

Observations of planets do not distinguish between the Tychonic system, where the sun orbits the earth and all other planets orbit the sun, and the heliocentric system. The only way to determine if the earth is moving is by stellar parallax: the triangulation of stars from opposite ends of the earth’s orbit. Galileo predicted stellar parallax but it was not observed for 115 years*, so his theory was falsified until then.

In fact, under relativity it is impossible to determine whether the universe has a centre, so it is a theological rather than scientific statement.

The proper way to consider Galileo’s work is not as a scientific result, but a shift to a new paradigm: astronomy based on telescope evidence with no reference to scripture. You might find this more elegant, it might be better at landing people on the moon, but there’s no basis for saying it’s more truthful.

* And even then it wasn’t stellar parallax, it was the unpredicted steller aberration. Parallax wasn’t observed until 228 years after Galileo’s prediction.