When I was in the Navy over 1/2 of all Officers came from OCS, a few weeks from college graduation.
My daughter went to a recruiter in 2010. They were trying to get her into Nuclear Engineering. When I asked the recruiter about OCS he said that of the officers that did not come in through ROTC, 95% came from the fleet. So, if your college did not have naval ROTC, you were pretty much screwed. Then he went back to talking about Nuclear Engineering. (My daughter had strong math skills.)
Back in the day it was similar when I tried to get into the Navy. It was almost the exact same speech. Its too bad they did not give that speech in high school-—it would have changed my college plans.