Welcome!
So theoretically you *could* sign the number of players you have openings (2, it appears) in the first session. And yes you would then need to wait until you can cut players after the season, when you’ll have open scholarships and be eligible to sign more players. HOWEVER, at D3 signing players early is not usually advisable. The reason is that you’d have to be signing D3 pool players, and most of your human competitors will be recruiting players from D2 and D1 pools. D3 pool players are best left to sims.
If you’ve already used your scouting funds for the year, and didn’t scout D2 or D1 pools, you can perhaps find a usable D3 pool player to sign, but I would think about waiting until the second session, cut a player or 3, then use that extra stash to scout again, but focus on higher levels.
Here’s how I recommend scouting at D3. For use in the second session, and next year and beyond. As you’ll see in the thread, other folks find other ways to be successful, but especially as you’re learning the game, I recommend starting with this, getting the biggest pool of level 4 players you can get, and then tweaking from there to fit your style and preferences as you get experience with the game.