Monkeys throwing darts can also (just happen to) be "right" when picking stocks that do well in the market. Galileo had as much evidence in believing Copernicus was right as the monkeys.
If he had simply stuck to simply arguing both sides of an hypothesis in his Dialogue, which he was asked to do by the pope in the first place, it would have saved everyone a lot of trouble. Heck, Kepler's stuff was already around for decades, and Galileo completely ignored it (along with Tycho):
* https://en.wikipedia.org/wiki/Dialogue_Concerning_the_Two_Ch...
If you want to argue 'for science' then Galileo is not a good example: the only thing he just happen to be right about was that the sun was the centre of things, whereas everything else in the Copernican system (including epicycles) was just as messy as in Ptolemy. There was no practical reason to switch systems, and no evidence to think it was correct.
At the end of the day the person who actually got things right was Kepler, and he kept plugging away at the problem because of this belief that the physical world reflected the spiritual realm (KGW XIII, letter 23, 35; 1595)
> In this way, then, the Sun, itself at rest in the middle and yet the fount of motion, carries the image of God the Father and creator. For what creation is to God, motion is to the Sun. Moreover, it moves [the planets] in a fixed place, as the Father creates in the Son. Unless the fixed stars offered a place, thanks to their motionlessness, no movement could exist. I defended this axiom while still in Tübingen. The Sun distributes motive virtue through the medium space, in which the planets are found: just as the Father creates by spirit or by the virtue of His spirit. And from the necessity of these presuppositions, it follows that motion is in proportion with distance.
See Kozhamthadam's "The Religious Foundations of Kepler's Science" and "Theological Foundations of Kepler's Astronomy" by Barker and Goldstein.
Going further, one needs to believe in certain metaphysical assumptions before you can even start doing what we know call science:
* https://en.wikipedia.org/wiki/Naturalism_(philosophy)#Provid...
There were plenty ideas floating around at the time, but ideas are cheap. Galileo certainly made important improvements to telescope technology, but his efforts in moving forward new models (specifically Copernican) were a dead end, and he made no practical difference to things: Kepler was already defending Copernicus in his Mysterium Cosmographicum (1e 1596), and put forward his laws in Astronomia nova (1609), a copy of which he sent to Galileo, which Galileo promptly ignored even two decades later when he published his Dialogue (1632).