I believe you have to have a parking pass to park next to the stadium and you can only get those if you’re a UTSA season ticket holder. You might have to find someone who has one, or one on StubHub.
Last time, I parked on the other side of I-37 and walked over. Not too bad, but it is a bit warm as you’ll be walking for a little bit. As far as I know, there isn’t a visitor’s tailgate area.