In NCS, the first day of practice was Monday, which means the first day of tryouts was Monday. Most schools go with three days of tryouts, and then teams are determined -- well, except for the kids running cross country or in postseason in volleyball, tennis, golf and water polo. They have to be allowed to try out as well, but can't do so until their season ends.
So a bunch of kids can conceivably show up next Monday, or the Monday after, or even the Monday after that, and get their three days of tryouts.
Usually, the varsity coaches have a good grip on the talent playing other sports, but, for example, I saw some freshman girls for the first time last night, and they are JV candidates I didn't know about. And then I have to wait for the varsity cuts. And then for the girls who will trickle back into basketball after their season ends (I know of two from cross country, but there could be more -- and some of the freshmen could be pretty good.)
Things are never as simple as they seem.