It's pretty simple stuff, sandpaper; just sand, glue and paper. So it's no surprise that it existed by the 17th c., though sand isn't as sharp as ground glass, or as hard as natural aluminum oxides like garnet, all of which were around and were also used. However, I think it is safe to say that it would not have been used the way it is now, with a woodworker going through sheet after sheet ( or disc after disc) to get a flat polished surface, and keeping piles of it in different grits. Old furniture and musical instruments show evidence of planes and scrapers first being used to get a decent surface ( and it should be mentioned that a cabinet scraper with a burnished hook edge is indeed very effective, and is still often used). Above that there are descriptions of rubbing with "dutch-rush" ( dried horsetail, a plant that had a lot of silica) and a kind of abrasive sharkskin to get a finer surface, or what might have been pumice stones. Above that, the surface might be gone over with a burnisher made of bone ( or, for small work, one made of a dog's tooth) . After the varnish was dry that could be leveled with pumice abrasive, and polished with a fine pumice that was called tripoli then, now called rottenstone.

Difficult thing about researching sandpaper, however, is that it's awfully ephemeral stuff, as it's cheap, and thrown away when worn and useless. And the hide glue binder is susceptible to being eaten by fungi or insects. Planes and scrapers survive, but I don't know if there's any very old sandpaper in existence. Even the contents of the Dominy shop, that went intact from the 18th c. into the Winterthur Museum, didn't seem to include any of it.

Stalker, John and Parker, George (1688) A Treatise of Japaning and Varnishing. Oxford.

Burnisher and scraper from the Dominy Shop Collection at Wintherthur