The basic qualifications for a Defense Engineer are similar to an Engineer in the private sector. They'll need a Bachelor's degree in some type of science, usually an Engineering or Chemistry degree. They'll eventually need a postgraduate degree in a very specific area, such as Nuclear Physics, Thermodynamics, or Aerospace Science. The degrees are only a piece of the puzzle. The competition is incredibly fierce and grades, internships, and job experience will be scrutinized.
And, of course, there are those pesky background checks. Hopefully you don't have major debt and your uncle isn't an outspoken sympathizer with a Montana militia.