My hat stretching instructions are crude, but effective.
You're just stretching the "slack" out of the "knots" in the machine-stitched  nylon threads that join the hatband seam(s).
you're not stretching the leather.
Once the slack is out of the seams, the hat won't stretch any further.
You can get maybe an extra 1/4" to 3/8" out of the circumference, so don't stretch too hard at first (you don't want to make it too big)
But you'll probably end up pulling real hard.
You're going to stretch the hatband in 4" or 4" sections, all the way around the hat.

Flip the hat upside down and grab the band with hands 4 inches apart.

 Avoid pulling on the seam in the back of the hat band.
Lift it towards your chin and pull straight outward firmly.
 Reposition your hands a few inches further along the band and repeat.
Repeat, repeat, yadayada, working all the way around the band,
 AVOIDING THE SEAM AT THE BACK OF THE HAT.
Try on the hat.
 If it needs more stretch, repeat the above,
but this time pull real hard (but not on the seam at the back of the hat).
 You won't pop the threads.
You should be able to get an extra 3/8 inch or so out of it.
If that's not enough, send it back and I'll fix/replace it.