This is a subject touched on in the book Galileo's Telescope (2012; first english translation 2015).

Very simplistically, they would have lacked the refined convex lenses that arose from spectacle making, an aperture to block out the imperfect ground edges of the lenses, and the intense determination of Galileo himself. Spectacles had been around for a while and were known and written about since the 1200s or so. The first mention of someone applying for a patent using these in a telescope was a person named Lipperhey from Middleburg in Zeeland. He applied for the patent at the Hague. However, just by coincidence, some of the best glass makers and spectacle makers were in Venice. And Galileo, coincidentally, lived in Padua near Venice.

The science and theory of how to put lenses together for magnification was known for awhile and recorded in a scientific encyclopedia called the Magia Naturalis (1589). However:

"Although [Lipperhey's] lenses were no better than those of other craftsmen, he must have used an approach that allowed him to remedy the problem of the lenses poor quality...a paper diaphragm with a small aperture in front of the lenses, thereby mitigating the optical distortions caused by inadequate grinding of their edges."

Galileo and a group of other natural philosophers got wind of this invention. Galileo went around to lens makers in Venice to procure lenses and when they couldn't produce exactly what he wanted, he began making them in his own workshop. There is a picture of a shopping list in Galileo's Telescope which shows items that were probably needed in the process: cannon balls, sand paper, and something to adhere the sand paper to the cannon balls.

Edit: Padua not Pisa. He was from Pisa.