Here's the way we do it in the Golden Knight Battalion.
June/July we send out initial paperwork (direct deposit, copy of contract to review, other forms).
I schedule a time to take the PT test (you need to pass an APFT to contract).
I travel the state during July giving tests/retests.
Friday before classes start we sign all the paperwork that still needs signing (contract), and we swear you in if you are otherwise qualified. I usually give a PT test that morning, for the last of the "haven't passed the APFT" crowd.
Some schools give the PT test to everyone on that first day/first week. You'll need to check in with your new Battalion to find out exactly how they do it. Some schools even have an orientation that lasts a couple days. For now hang tight just a little longer. Us ROOs are finishing up the school year/scholarship process. Once the semester ends we can shift fire to the incoming class, and I'm sure you'll be hearing from your new unit.