It's never too early to start training, and if the martingale collar is sized properly, he should be fine (with the collar on, pull the ring on the chain till the collar is snug. There should be one to two fingerspaces between the two rings attached to the material). If you're worried, just put the collar around your own neck or arm, and you can see what it feels like. They always seem so fragile as puppies, but you'd be surprised at what they can handle. Holding onto the leash to "soften the turns" actually defeats the purpose of the training, as they wouldn't be corrected properly. It's called handsfree for a reason

Don't worry, if he's pulling, he's more than capable of stopping the pulling to keep up with you and ease the tension on the leash and collar. And above all, enjoy your new puppy and the time you get to spend together training!