UCSB has a great CS department, and a lot of the professors are happy to have undergrads work in their labs.
My son is a HS senior who has taken a couple UCSB CS courses (including one of those upper division “majors only” courses). A lot can be done at UCSB by talking to the professor and asking for an “admit code,” which lets you add the class even if it is full. And, it always pays to be nice to the departmental secretary!
Math classes will likely be his largest classes unless he takes honors sections (proof-based and mostly for math majors I think). My son took linear algebra in a 600 person class, but the sections that met separately were ~25 people and he says it wasn’t bad. That large hall/theater seats 860 people, but 600 is the largest I’ve seen listed.