Not sure if they come out with a major in engineering, but, I think they do, at least, come out with a minor in it.
Jumping in way late here to say that USMA cadets can major in lots of stuff other than engineering, and many (probably the vast majority) don't have a minor. My major was Mathematical Science and I didn't have a minor.
All cadets, regardless of major, take core courses + an engineering sequence -- the Academy calls this the "professional major." The declared major (Nuclear Engineering for Toth) is the "academic major."
Core courses include what you might expect -- 2-4 semesters of English, math, history, etc., and some that wouldn't be considered core courses elsewhere like 2 semesters each of chemistry AND physics (there is no "take at least one physical science" thing at West Point), 2 semesters each of history and
military history, a semester of law, .... The engineering sequence is 4 semester classes in one of several engineering disciplines like civil, mechanical, nuclear, .... , or even cyber.
All of that required math and science means that even our English majors graduate with a Bachelor of Science degree rather than a Bachelor of Arts.
