Galileo did not invent the telescope. He heard of the Dutch device in 1609, built better ones than anyone else within months, and did the thing nobody had thought worth doing: pointed it up and published immediately. The Starry Messenger appeared in March 1610 and is a short book with enormous consequences. The moon is not a polished sphere but has mountains and valleys, with shadows that shorten as the sun rises on them. The Milky Way is not a vapour but a mass of individual stars. And Jupiter has four small bodies going round it, which he named for the Medici.
Later work added the phases of Venus and the spots on the sun. Both mattered. Venus showing a full set of phases, from crescent through gibbous to full, is impossible in the Ptolemaic arrangement, in which Venus never gets to the far side of the sun. Sunspots meant that the heavens change, against the doctrine of an incorruptible celestial region.
The honest qualification, which is usually left out, is that none of this proved Copernicus. It disproved Ptolemy, which is not the same thing, because Tycho Brahe had proposed a system in which the planets circle the sun and the sun circles a stationary earth, and every one of Galileo's observations fits it perfectly. His opponents could and did make that point, and there was no stellar parallax to answer them with. He was right, and the case he could actually demonstrate in 1616 was weaker than he claimed.