Please!!
Those closest to the situation make the recommendation. If the lower-level folks OK, the upper-level guys basically sign off on it, just to get it off their desks.
During my military tenure, if my leading petty officers and Chiefs approve leave for junior sailors in my division, I simply approved it and passed it up to my Department Head. Barring some emergency or unusual situation, the executive officer and commanding officer OKs the leave request.
Heck, in most cases, it never makes it to them because they've authorized the department heads to be the final stop on leave requests.
ok, you want to fantasize that Westmoreland would have then had to ask the Secretary of the Army (or someone else on that list to nominate him)
fine, let's entertain your fantasy
then Carson would have had to apply
of course he was never nominated and never applied
then he would have had to compete against all the other applicants
again, he was never nominated and never applied
but all that is just a mere formality
I met an astronaut when I was a kid and he told me one day I could be an astronaut too
I now tell people NASA offered me a job as an astronaut but I turned them down