I would say closer to 6ish for finding sports they may or may not like. 3 year olds can barely be attentive for a circus, nonetheless a team sport. Persistence at this age on your part would be a grave mistake.
Honestly, I would avoid trying to develop anything outside of stuff your child shows an interest in at this age. If he likes bugs...study bugs. If he likes to ride bike, take him biking. Once he gets a little older (kindergarten/1st grade) try a sport, keep him in it for the entire season no matter what, with the disclaimer that if he doesn't like it he doesn't ever have to do it again...but he must finish the season. This way he gets into truly learning the sport or activity (instead of quitting before he even understands the fundamentals). If he doesn't like it, try something else next season. Don't push besides making them finish the season they start.
Kids find their own way...and I personally don't think you should force athletics or anything else on anyone. Your best bet is trying a few things as he gets older, and when he shows a real interest or affinity for one or two...focus on those. If he shows an aptitude for something then focus on that (be it sports, drama, singing, whatever...).