The Engineered Century by Neil Armstrong (2000) [pdf]

"He earned a student flight certificate on his 16th birthday, then soloed later in August; all before he had a driver's license."

And he got his MS 15 years after his Bachelors, although it was in aeronautical engineering. As for Aldrin:

"Buzz Aldrin graduated third in his class at West Point in 1951, with a Bachelor of Science degree in mechanical engineering. He was commissioned as a Second Lieutenant in the United States Air Force...."

He got his Sc.D. in astronautics a dozen years later.

I think they had to be both serious pilots and engineers to succeed in the Apollo program, e.g. note Armstrong's diversion from a boulder strewn field during the descent.