A lot of guys on here force carb and have drinkable beer much faster than the set and wait method. Here is a good video on it.... somethink to think about:
https://www.homebrewtalk.com/f35/kegging-force-carbonation-video-233233/
I force carbed a keg yesterday and will probably hook up the beer line and give it a taste tonight. Depending on how carbonated it is, it might be better tomorrow or even the day after but I personally like tasting beer through the carbonating process as well as the brewing process to help me get a better guage on excatly how my beer tastes after day 1,2,3,etc. Technically, after force carbing, the beer should be good and carbonated the next day, but i find that once I turn the PSI back down to the serving level, it still takes a few more days before the beer is optimal.
This is just how I do it... not necessarily the right or best way to do it. I also would have already had that beer kegged after 14-16 days but I wont get into that