There is no arguing that there is something special about Galileo that has placed him in a certain place of respect in the minds of the majority of the population today. However when his ideas and methods are evaluated he doesn't come off as being an outstandingly brilliant scientist. I think that the reason that he is so revered and seen as the pioneer of the Enlightenment today has more to do with his personality than with the merits his scientific argument brought forth. .
The idea that Galileo is most widely known and accredited for is proving that the Earth is not the center of the universe like it was thought to be. Rather, the Earth and other planets revolve around the sun. This idea was not even the work and ingenuity of Galileo, Nicholas Copernicus. Despite the objections he received in trying to promote the Copernican model of the universe, the model was still borne by another person. It must have taken a great mind to conceptualize a system of the universe so different from the one that was constantly being taken as true. This idea is one in the spirit of the Enlightenment, but Galileo wasn't the one who thought of it.
Another aspect of the Enlightenment that Galileo is credited with being a pioneer in is the idea of using empirical evidence to prove a point. The evidence gathered by Galileo to support his claim of a heliocentric universe was not strong. The strongest data that Galileo used was the fact that Jupiter had moons revolving around it and therefore the Earth wasn't the only body in the universe that had objects revolving around it. From there Galileo shows that if we were to take as granted that the sun is indeed the center of the universe, there would be a vast reduction in the amounts of epicycles that need to be used in following the movements of the planets. This whole argument rests on the fact that the finding a simpler way to explain the world is always the better way.