I agree with Juillet, gaining proficiency in high school math is the result of lots and lots of problems, not just some innate math talent. You can be a bright but ordinary student and gain the base for engineering.
The end goal for high school is to build a solid foundation to study engineering There is no need to calc BC, linear algebra, DE. In fact, unless the high school has a fully qualified math instructor who truly knows linear algebra and DE, I’d avoid these classes. I’ve seen some disastrous instruction that probably put the students at a disadvantage because they think they know linear algebra when, in fact, they don’t.
Tutoring with additional problem sets will definitely help the boy but it won’t suddenly push him forward a year. Offer to pay for the tutor but otherwise choose your actions/offers carefully. .
Follow the boy’s lead. If he is capable and wants to go faster, great, but make sure he has the proper prereqs. Community college may be a great place to start, especially if your state flagship (or state schools with engineering) has transfer agreements with the community college.