Agree with
@scprepoh. In many ways recruiting at a service academy is the same as any other school. Fill out the questionnaire, contact the coach, etc. Good chance you'll end up on a mailing list and receive general info from the program or canned emails from the coach that may go to all recruits. You may get a personal email from the coach, but don't be discouraged if you don't especially if it's early. Much depends on the sport and recruiting resources of the team. Many coaches don't put full effort into recruiting the next incoming class until the season is finished.
Also like any other college, a coach can't "get you in", however, they can advocate for the recruit during the admissions process. I think this is where service academies start to differ a little. At many civilian colleges, it's mostly about grades and maybe test scores and there's a fair amount of wiggle room (especially if we're talking about typical non-high academic schools), so being a recruited athlete may go a long way.
At service academies, particularly what I've heard from Coast Guard coaches is, they sort of get used to just taking what they get and making the most of it. Admissions standards are very high and include not only academics, but athletics, leadership, etc. It's not to say they don't put effort into recruiting, but I think they're well aware they could recruit complete studs, but if grades and the rest of their application is weak, it's almost pointless. Class size is very limited too. Especially at CGA, so not a lot of room to move.
CGA has a number system they use for sports recruits. Generally speaking, a 3 is a complete game changer, a 2 is a solid contributor, and a 1 is good enough to be on the team. There are benchmark numbers for each team they try to hit that's part of the admissions review process. This is obviously a moving target as kids graduate each year and new kids enter the program, so the number/quality of athletic recruits they're looking to plug into each sport will vary year to year. It will even vary some within the admissions cycle based on appointments offered/accepted/declined. For instance, if a recruited athlete for a particular sport declines their appointment sometime in April, admissions may be looking to the waitlist for another kid in that sport to fill the void. In a pool of many highly qualified candidates, it often comes down to luck of the draw based on current needs of the service.
The fact your son has times in line with CGA is great. He just needs to keep working, and make sure he's well rounded with grades, highest level STEM classes he can handle, and extracurricular activities with demonstrated leadership opportunities.
I'm not sure what grade he's in, but if he's currently a junior, he should apply to the AIM summer program at the Coast Guard Academy (application for this summer is open now). AIM has a competitive application process, but Coast Guard coaches can advocate for applicants in this too, so another good reason to establish contact with a coach. If he's not yet a junior, make sure AIM is on his radar for when he is.
Good luck!