White-labeled Dreamcast games are the oldest Dreamcast games in America, with the orange-labeled All-Stars being second eldest and the black-labeled ones being newest. However, that depends on the game's print run(s), e.g. some only ever had white labels, but were printed for a few years, say 1999 - 2001.
My advice would be to get a small flashlight without too bright of a bulb (so as not to hurt your eyes) and shine the light on the top the disc. Then, from the opposite side of the disc, see if you can see any little streams of light poring through the disc. If you can, then you have bit rot, as those streams of light are allowed by little holes forming in the metallic layer of the GD-ROM.
Thankfully, Sonic Adventure shouldn't be an expensive game to replace. I suggest this eBay auction:
https://www.ebay.com/itm/DC/232650088244 That way, not only will you get a disc-only copy of Sonic Adventure, you'll also get disc-only copies of SEGA Rally 2 and Trickstyle and a sealed copy of PlanetWeb 1.0. Plus, mixed lots like these don't usually sell for much as people usually only want one specific thing and not a bunch of random things.
Ethnically, though, I'd say you are in the clear if you want to burn a CD-R copy of Sonic Adventure. Why? You own a legitimate copy of Sonic Adventure, so why should you have to pay twice just to play the game? Either way, though, I support you.
