You probably need to go directly through the dealer. They know who will and won't work with you and can make calls to get special approvals.
Some people have had luck with Capital one right after discharge, but terms seem to be so-so.
The day after discharge we were approved through Chase on a new Mazda. I'm sure had we applied through Chase we would have been denied, but the finance manager was able to make some calls, explain the situation and get an approval.
NFCU Rewards - $18,000, NFCU Signature - $18,000, NFCU LOC - $15,000, Care Credit - $7,700, Lowe's - $6,400, Capital One QS - $5,000, Walmart - $5,000, Amazon - $4,000