Short answer - difficult, but not impossible.
Long answer...
"Hawsepiping" (non-academy grad) your way to a 3/M license is becoming increasingly difficult these days, as well as expensive, even for experienced civilian mariners.
Meeting the sea service requirements depends on what you do in the Navy. If you were an officer, I can tell you that you would almost certainly need to be a SWO. I'm not sure what would be the best rate on the enlisted side. Being a desk jockey won't cut it. Also, AFAIK, you cannot get any STCW requirements done using strictly military service - except maybe Basic Safety or Firefighting. You would need those courses to get a 3/M license and the cost for them would come out of your pocket (to the tune of thousands of dollars), unless you're VERY lucky and find an employer willing to pay your way through it. I believe you can get some assessments signed-off onboard by OOD's, but you can't escape the course requirements.
Don't expect much "sympathy" from the USCG/NMC regarding this. The MM credentialing side of the USCG is quite different from the military side. You could also have to start off with a limited license and then work your way through to the unlimited ones. As someone who has seen both worlds, there is a reason this is a "difficult" transformation - the two sides (Navy and MM) are quite different.
If you really want to go in the Navy but maintain/keep a 3/M license, you would be way better off going to Kings Point or a state maritime academy and joining their MMR program (get a degree and commission too). Graduate with your license and commission, go Active Duty, become a SWO - keep yourself in a "maritime-like" billet to the extent that you can. You can maintain your license even while on Active Duty. Much easier to do it that way than the reverse (Ie, Navy to MM License).
Also,
gcaptain.com is a great resource for the credentialing/licensing process and there are a number of threads about making the transformation from Navy to MM. There are also threads about general MM life, jobs and the state that the industry is in right now. Poke around.