Yeah charcoal may help clear it up faster... but you would want to pull it out once you get plants in there -- carbon can suck of some of the valuable ferts your plants need.
Aqueon water clarifier (or similar products) also work if you want it to clear as fast as possible. It will bind the particles together quicker so they sink/get filtered out much fast. Ordinarily I wouldnt suggest it, but since you don't have any fish it won't hurt anything.