Tough $hit. You enlisted in the Navy, now go.
I agree but want to clarify your terminology. He did not just enlist, he has just completed 4 years of being PAID to attend an entirely free education ranked among the best in the world. He knew GOING IN that if he got beyond his first year, he had a minimum of 3 years enlisted service should he fail to get an Officer's Commission. Upon graduating he has the standard 6 years minimum service before he can try baseball.
He does have a potential out in that if he refuses a Commission and the Navy agrees that they want him gone, he can pay back the US Taxpayers the cost of his education. If the Navy still wants him however, he gets to be a sailor for 3-8 years of active and/or reserve service. My bet is that he will be invited to play Navy Baseball to keep skills up and he MIGHT get dispensation in 4 years to do the rest in a LONGER Reserve term.
David Robinson (USNA 1987) got dispensation from the Navy to go into the Reserves 2 years after graduating and then joined NBA San Antonio. A reason given was that at 7 feet he was just too large for many duty assignments. FYI, he joined the Academy at 6 ft 7 in, which was 1 inch under maximum.