The Dutch invented the telescope, and those made by a particular Dutch eyeglass maker, Hans Lippershey, were in common use by 1608. Galileo heard about the discovery in 1609. Without ever having seen a telescope, he constructed one of his own, legend has it, overnight. He quickly built other instruments; his best having a magnification of about 30X. His telescopes were not even as good as a pair of modern binoculars.
The usefulness of the telescope for terrestrial observations and military applications was readily apparent to many people. But the idea of using the telescope to observe the heavens was less obvious. There was a long tradition that the human eye was the best possible measure of truth, while lenses and mirrors produced distorted images and sometimes even made things look upside down (hence today's expression "it's all done by mirrors" to imply someone has tricked us). Galileo made many tests to make sure his telescope was giving an accurate image. He was then one of the first to turn a telescope upwards and make careful and detailed observations of the sky.