Been too long since one of mine was an undergrad to remember exactly how registration for freshmen works, but I want to warn you that some lab classes (esp Ochem) are impacted and it may be difficult for your son to enroll in required science labs as a freshman. Priority for labs goes to upperclassmen and students who have already completed the lecture portion of the class.
I also wanted to warn you to be careful about trying to use professor overrides to get into filled class sections. UNM has --or at least used to have-- a policy limiting the number of overrides a student could use during undergrad. IIRC, a student had a max of 5 red cards to use during undergrad. Once those were used up, you’re out of luck.
Professors must allow admission into a class with a red card so these are typically used by upperclassmen trying to get their graduation requirements done on time. Red card priority is given to seniors and those close to completing graduation requirements. A red card can bump a lowerclassmen out of class in order to make room for a red card holder.