At such a small size you can start training them to eat pellets and also mix their diets up with some of the following frozen foods:
At 5" and less: bloodworms / pellets / chopped up frozen foods such as shrimp / mussels / clams etc but take the meat off the shell...
As your puffer gets larger, you could feed your puffer clams with half shell or pryed open with full shell (if the shell is not overly thick) / mussel on half shell / crayfish (smaller than your puffer) / river prawns / squid etc...
Pellets would be the best thing to get them on as a stable good and then you could use frozen foods to mix things up...