If you sign up for one of the credit unions offered in boot camp (Navy Federal or Armed Forces) you will have the card and be able to spend money by liberty weekend (the time between graduation and shipping to school). If you elect to keep your hometown bank you will be able to sign up for direct deposit while in boot camp.
A word about Armed Forces Credit Union: I haven't seen a single branch or ATM in my time in the Navy, which has included being stationed or pulling into Pearl Harbor, Norfolk, Groton, Portsmouth NH, Brunswick ME, Guam, Charleston and Okinawa U.S. military bases. If you want fee-free ATM access and local branches go with Navy Federal or Bank of America (BoA isn't offered at boot camp, you'll need to get an account before you join if you want it).