When we did the 10der and mild swap, it was 10 days from grain to shipped out to the recipient. So, it fermented in about a week, then was kegged, forced carbed and consumed on day 10. It was good! A lower gravity beer, without a ton of hop flavor, will be ready to drink sooner than some bigger beers that need some time to mellow. It also helps if you use a highly flocculant yeast strain, so that the yeast falls out quickly.
I think the very first brew I ever made went into the bottle 7 days after I cooked it. It wasn't enough time. I had quite a few tops popping shortly after I primed and capped...