The "traditional" story (the one that "seems most likely" because we don't really know) is that some kids were playing with discarded warped glass at a glassmaker's shop and ended up with a magnifying glass or rudimentary telescope. Enter the simultaneous invention of the telescope in multiple places (very likely it wasn't any one person in particular), Galileo starts using it for scientific stuff, now they're making lenses on purpose. Old nearsighted lensemaker looks through it, maybe some charts or a book on the table, all of a sudden they can see well. Attach to frame. Glasses.