Your commitment as an NFO will most likely take you through a sea tour and a shore tour. You won't have the time to get the prereqs done until at that short tour. You'll want to do your best to get to a station that has a college where you can actually take the prereqs you'll need. Knock those out and take the MCAT. You can apply to USUHS while still on active duty, but it is unlikely you'll be able to resign before your commitment is up so you should plan on applying for the class that will start after your commitment. You'll resign and recommission and then PCS to the school. You can do it with no break in service.