I enlisted at 25 after teaching high school algebra for three years and have a math bachelor's. I've been in 8.5 years and was just selected for E7.
Sounds like your son has no real direction, so screw the enlisted route and go officer. If he enlists, he will get to pick his career field. Infantry enlisted will give him zero marketable skills. Their service is appreciated, but as far as transferable skills, he won't have many. If he was really passionate about something, then by all means enlist and get that job. Otherwise he should go the officer route and make a heck more money and gain a lot of the leadership training that he can market when his service ends. He will most likely wind up in a combat arms career field, but it will be at the management level, not grunt level.
It's silly that you're this involved in his decisions, but that's a different conversation. Ask the Army recruiter about OCS (officer candidate school) and that timeline. Do a google search for military pay and benefits and you'll see the drastic difference between an O-1 and E-4 (your son should start out as an E4 because of college). If he's enlisted, he will live in barracks with 18 year olds and have his life micromanaged for years until he gets promoted to E6 or marries a stripper. The quality of life and pay are better for officers and the skill set he will gain will set him up for a better career outside the military.
Again, it comes down to passion. If he doesn't have one, then follow the money.