Theoretically, yes, your beer could be drinkable after only 8 days. Meaning, nothing is going to stop you from going into bottles or kegs at the 8 day mark, and what you will be consuming will by definition be beer. Hopefully fermentation completed, and you don't have bottle bombs. Using the term "green" flavors is a very subjective term, for both personal tastes, as well as the beer style. One of the big things that contribute to a beer's green flavor is diacetyl, which goes away around 3 days (give or take 1) after fermentation has completed. You should not remove the beer of the yeast cake before the diacetyl rest has completed (meaning 3 days have passed since you hit your targeted gravity). I like to assume 7-8 days for primary fermentation and diacetyl rest to complete.
There are other ways people use the term "green beer". One example would be the style of beer dictates how long it should mature before being drinkable, or not green. Extreme examples would be barley wines or Belgian quads. These mature over the course of months, if not years, where as an IPA can be ready to drink (meaning kegged or bottling dates), dry-hopped and everything, inside of a month.
Realistically, to answer the title question, it depends. If you are brewing a hoppy IPA, you want to drink it fresh. You could have it go into a bucket, and come out of the bucket for kegging or bottling in 2-3 weeks. Another 2-3 weeks might stand to help, but if you want fresh, that could do it. On the other hand, if you are brewing a stout for Christmas, you might want to get started now. Stouts benefit from spending time in the bottle, and get much better over the course of a year if stored properly. Each style is different, and will have different flavors depending on how old they are. If you're looking for a quick fix, look for light alcohol, potentially high IBU (although IPA's or Pale Ales aren't the only kind), session beers. Those will be what will most often be the quickest to drink.