I need help stiffening and smoothing out my hat...HELP?

have you tried blocking it? if you treat it with steam, while it is over a mold shaped the way you want it to be (a ball?), and smooth it with your hands, That should help. If you don’t have a steamer, and I’m going to assume you don’t, I would try boiling some water and holding the hat and mold over the steam from the boiling water. If you don’t feel safe doing that, Try your luck with hot water and a little soap. Good luck! I’d love to hear how it turns out.