According to ThoughtCo (and many other sites):
Glass that is transparent to visible light absorbs nearly all UVB. This is the wavelength range that can cause a sunburn, so it's true you can't get a sunburn through glass.
However, UVA is much closer to the visible spectrum than UVB. About 75% of UVA passes through ordinary glass. UVA leads to skin damage and genetic mutations that can lead to cancer. Glass does not protect you from skin damage from the sun. It affects indoor plants too. Have you ever taken an indoor plant outside and burned its leaves? This happens because the plant was unaccustomed to the higher levels of UVA found outside, compared with inside a sunny window.
For reference, the definition of UV-A and UV-B is:
The UV region covers the wavelength range 100-400 nm and is divided into three bands:
UVA (315-400 nm) UVB (280-315 nm) UVC (100-280 nm)
My skepticism comes from the fact that no one seems to reference a primary source to glass being transparent to UV-A rays (or non-transparent to UV-B rays, for that matter). Is there a lab that actually tested different types of glass/plastic to determine how much UV light passes through each or is this all based on "common sense" without serious measurements to back it up?
NB: Is it possible to get a sunburn if you're behind a (glass) window? addresses a similar question but I don't think its a duplicate per se.