No, Galileo did not discover that the Earth was round. The understanding that the Earth is round dates back to ancient civilizations, well before Galileo’s time. The roundness of the Earth had been established by Greek philosophers like Pythagoras and later confirmed by Aristotle in the 4th century BC.
What Galileo is known for is his improvement of the telescope and his astronomical observations, which provided valuable evidence for the heliocentric model of the solar system proposed by Copernicus. Through his observations, Galileo noticed the phases of Venus and the moons of Jupiter, which challenged the prevailing geocentric view.
In summary, while Galileo made significant contributions to our understanding of the universe, he did not discover the roundness of the Earth; that knowledge was already established thousands of years earlier.