I think my savings account sent me some checks when I opened it. Of course Reagan was in his first term then too so perhaps things have changed.
I've had to do something similar, I just wrote a check from my checking account and transferred it online from savings to checking. If they're both USAA it is instantaneous.
You could get an official check, but that takes a few days to mail to you. https://www.usaa.com/inet/pages/g_old_Bank_Official_Check_Request_index
Enjoy your new car!