Title. Is it possible? or Auto Reject?
Read Academic Preparation | Undergraduate Admissions and ask them directly if you are still unsure.
The freshman math class at Caltech used to be held in their largest lecture hall. If it’s still conducted in the same manner, with all 200+ students, then your son will have difficulty with the coursework, when compared to the rest of the class.
Caltech’s admissions are based on the whole application especially the essay. Math skills have to be as good as humanities and social science skills.