Eight weeks old is when training should start. These days reputable breeders are starting their puppy imprinting at 3 weeks until the dog goes to their new homes. Obedience training can be started immediately. You do not have to wait until the dog is mature in order to train them. Formal learning should start with positive reinforcement training the moment your new puppy arrives in your home. Do not wait until they are 6 months or older to start. Get started right away.
Simple, the earlier the better. Dogs learn from repetition and consistency. A dog that started training at 8 weeks and has consistent training will be set for long term success.
I start puppies with sit, down, leash training and coming when called. Leash training is nothing more than attaching a long light leash to the puppy and letting them drag it around. This prepares the puppy for leash manner training later on when they are able to get out and roam the world with me.
Sit, down, and coming when called are a snap at 8 weeks of age. By starting these behaviors early you will help your pooch retain the behaviors over the long term because these months are their formative months for learning.
Tilt the odds in your favor and catch your pooch while their minds are fresh and eager to absorb the lessons.
Subsequently, if you adopt an older dog you can start training them immediately as well. No dog is too old for training.
The Pit Bull Training Handbook