So are you planning on constantly moving him to larger tanks as your puffer grows???
The reason i ask, is because when young they are still fairly easy to transport from tank to tank, but as they get older and bigger, its harder to transfer them without risking them gulping in air...
So my suggestion would be once he gets large enough for its final tank, maybe 6”-9”, i would place him / her in there and leave them there to grow up (unless there are other predators which can still get to your puffer even at that size)...