with a DAT from 22 or more, you can apply and board for navy HPSP scholarship without an official admission letter because you are considered as provisional acceptance dental applicant. without this DAT score, you wait until you get your official admission letter then you board. early acceptance allows you to board for october board without this, you wait until your first admission letter (dec 1st) and then to be boarded.
I don't want to get your hope up but chances are you won't board for october board if you meet your army recruiter tomorrow because tomorrow is already september, you have to fill out a lot of paper work, order your transcript and DAT score (which will take around 2 weeks), and schedule for MEPS (some recruiter is slow with this) and then if you happen to fail meps, that could take another 1 month. get your official hand signed LORs in to recruiter (portfolio letters dont work here), then more time is needed for your recruiter to do other paper work (such as verification, history check up, criminal back ground check)
I see you goes to a small liberal art college Whittier, which is just right next to where I live LOL. You lost interest in the big university in so cal?