At least 2 days, up to a week depending on how quickly you think they're actually hiring. My company is slow as f*ck doing hirings, we take apps for a few days, call back people about 2 weeks later, have them in for interviews for a couple weeks, take 2 weeks to decide, then offer someone the position to start in 2 weeks.
It's normally 6-10 weeks after we post a position before someone starts working for us.