Every child is different on when they start riding with training wheels and without. MOST important, especially since they are learning, is get a helmet, and make sure it fits properly. It should not shift in any direction if it is fitted and put on properly. It saddens me to see kids out there with helmets on, but they are sitting on the back of the head with the full forehead exposed.
The second most important is to make sure they are wearing proper shoes (not flipflops or croc type) I watched our neighbor girl fall and then she started screaming as she was barefoot and her foot slipped in between the chain and wheel and was STUCK! If she had been wearing shoes, her little foot would not have done that.
My 4 year ols has been riding since he was two, and is still with training wheels, which is fine, he is not ready. But he knows he does not get onhis bike with out his helmet and shoes and when we find him trying to do so his bike gets put away for the day, it only took a couple of times of taking it away and he is now a champ at riding with his gear on!