It all depends on the weather. I'm in Michigan, so putting poults in the coop before mid-April is risky. But because my post-hatch box is a plastic tote in the guest bathtub, I move them out as soon as I can, no longer than two weeks after hatching and ideally around a week. This lets me ensure that they are eating, drinking, and their lungs are matured enough to handle the temperatures, dust, and breeze in the coop. While they are inside, they are handled a lot.
Once they are in the coop, I try to spend at least three 15 minute sessions a day feeding, watering, and observing. While they are relaxed, I pick them up and handle them. With this treatment, I end up with mature turkeys that I don't have to chase, that don't freak out when I come in the coop even at night, and that I can pick up and handle with no problem even as mature toms during breeding season. And my husband and daughter, who don't spend much time handling them when they are little, can also pick them up and handle them with no issues.
Before I started this handling program, I had birds that were hard to catch and pen, that would slash with their wing tips, that would kick and peck, and that were just plain dangerous when scared. I don't want the turkeys to imprint on me, but I want to develop a trust relationship early. That way, they act like turkeys but are socialized with people as well, much like a horse is once trained.