You do not have to wait until you have a particular size group, in order to hunt. Back when I used a recurve, on my best day I couldn't shoot a 3" group at 20 yards, so I always made sure my shots were closer then that. I've shot many animals with a recurve, but the average distance probably wasn't over 8-10 yards.

All anyone has to do, is make sure they don't shoot until the animal is within their effective range, whatever that distance happens to be. Even a beginner who has only practiced a couple weeks should hunt, if they limit their shots to what they know they can make.