The scouting process usually produces a rookie official between 40 and 45 years old. Sometimes an official is hired in his late 30s, but that's pretty rare.
Since Ben Dreith sued the NFL for age discrimination, an official can work as long as he wants. Officials usually retire between 60-65 years old, although Bob McElwee retired at 67, Jim Quirk at 68, and Ron Botchan in his late 60s.