I should have posted this earlier but I got sidetracked and just now remembered it. I had this same concern too because I have procrastinated about getting a passport. I knew I might need one, but didn't think that A) It would take that long to get one and B) that they were so expensive. After reading this thread, I figured I better check into getting one ASAP.
So I sent an e-mail to Ryan Maloney--the contact person at Sony listed in the GT Academy travel itinerary. I asked him when the finals at Silverstone would take place, and he said it would be late May or early June, and that I should have plenty of time to get a passport.
I just wanted to let everyone know that if you don't already have a passport, you can wait until the finals in Orlando are complete before you apply for one and you should still get one in time to make it to the finals at Silverstone 👍 To be honest, I don't know when I'll ever need one if I don't wind up having to go to Silverstone for the finals, so I don't want to spend $210 for a passport that I don't need right now.