The lens is the core component of the telescope and the microscope. To make one, you need a fine abrasive, glass (clear or coloured) and some time shaping them.
Telescopes are immensely helpful to astronomy, navigation and surveying, so much so that once you have one, you're not going to forget how to make one.
Microscopes make cells and microbes very apparent, so it's hard to imagine anyone in history having made one until a little before germ theory.
These 3 points form something of a paradox to me. They are so easy to make, so useful, yet we know they're a fairly recent invention. I would've thought as soon as you had glass, the way it warps light when not straight, someone was going to try shaping and end up with a lens.
Am I missing something?
This question is better suited to Askscience than askhistorians. At the risk of speculating, I'd say that the early invention of telescopes and spectacles would suggest that there's something else missing--perhaps a precise understanding of refraction and magnification.
Microscopes make cells and microbes very apparent, so it's hard to imagine anyone in history having made one until a little before germ theory.
This one is slightly circular; the fact is that the a microscope could only be used "a little before germ theory"--because once good microscopes are invented, germ theory is sure to follow.