Which part? The bacteria will begin establishing themselves as long as there is a food source. Algaes come next, with stony tube worms falling somewhere between soft algaes and coralline algaes, IME. Other critters--mobile ones like pods and worms and stars--will begin moving in immediately.
However--"how long does it take for dry base rock to look like good live rock" is a different question. A minimum of 6 months, but up to a few years, depending on conditions and space.