@Pixie.RN is correct you need to speak with an officer recruiter, specifically a healthcare recruiter.
I spent 6 years active duty in the Navy's Nurse Corps and loved it. I look back now and wonder why I got out, but it does take a toll with travel/moving around every few years/not seeing family from back home, etc. I deployed to Afghanistan and I was stationed on a Carrier for 2 years. It was some of the coolest times of my life!
As far as being a brand new nurse.... that might handicap you a bit since there are many other applicants with experience who are clawing at the door to get in. I was almost immediately picked up since I had 8 years of ICU nursing behind me prior to joining AND I had my CCRN. You have to make yourself marketable! Any certifications, etc that you can get to make yourself stand out will help.
But, you must first start with talking to a recruiter (and the RIGHT recruiter). An enlisted recruiter will not be helpful and they may even try to sell you on "enlisting" first to get your foot in the door. Never believe this it is a total lie, those people are only trying to make quotas. If any recruiter uses the word "enlisted" you should be extremely wary.
Also -- Just because your program is "accredited" there are programs they do not accept. I graduated from a state university with my BSN so this wasn't a problem but I specifically remember them looking up my university to make sure it had a Regional accreditation (i.e. The Southern Association of Colleges and Schools). Some schools have shady regional accreditation (not nursing specific) that the US Navy just doesnt accept.
If you can shoot me a PM with your location I can take a quick look and see if theres a recruiter nearby.