Football I would expect to be during beast. They have their training camp second part of the summer leading into the academic year to prep for the season.
That said, depending on the sport and their need, walking on during the academic year may also be possible. I would recommend that you reach out to the coach in charge of recruiting for the team. One, it gives them a heads up that you’re interested so they know to actually look for you, and two, if other opportunities show up to try to earn a spot on the team. I know a couple people who ended up working out with a team during their off season during the school year and got picked up to play for the team after not making the initial cut over beast.