Yeah, there's no set time. I think that I joined a little bit before eofpi, and he's been an admin for a while. I have never been an admin. Counterexample right there.
Generally, adminship is determined by maturity, need, and demonstrated ability to govern fairly. How the admins are chosen on NP I don't know. Or care. The point is not the power, and there should be no yearning to be an admin. If there is, you're probably not right for it.