There's a stark contrast here between kegging and bottling. Bottling, few people are willing to even bottle before two weeks for fear of bottle bombs, then you typically need several days - at best - to carb up, so it's difficult to get a bottled beer from grain to glass any faster than about three weeks, and even then it's dicey. Brewers who keg and force carb can easily get lighter beers grain to glass in ten days, and I've heard of one-week turnaround beers - even if it's still a few gravity points from finished, it'll carb fine in the keg and there's no risk of bombs.
That said, as a bottler, the earliest I've cracked open one of my beers was after about a month, which was three weeks primary, one week in the bottle. I've done it with a couple brews, one of which was barely carbed at all, the other of which was nice and bubbly already. I could crack one of my Caramel Amber Ales today and beat that record by a week (two week primary, one week bottled), though I probably won't. On the other hand, the batch I've currently got fermenting will probably be bottled by the two-week point, and there's a good chance I'll crack one after a week.