It's a ....Froggy character cap?
Indeed, of all the (fairly) obscure characters to choose from, here comes a Froggy hat. This is a 'character cap' style, where the hat itself is made to resemble the character's head. It has the eyes on the front, the yellow top marking, the two side markings are on the back & there are also the cheek dots. The bill is right below where the lip would be.

The hat is a curious choice but....
It DOES come with an explanation. If you watch the little shorts Sonic 'cartoons' on Youtube, you'll find the Team Sonic Racing ad / mini-show. In it, Eggman tries to trick Big (of Team Amy) into quitting the race by putting up a "Frog Merchandise Stand" with all frog themed items. This cap, and the t-shirt are among them. Wacky hi-jinx of course, ensue...but what's even wackier is that the Sega Shop decided to make the hat a real thing.
This hat is about FORTY dollars! Plus, Froggy is fairly abstract to begin with so it's almost in "Secretly-Sonic" territory where even a big fan might not recognize what the cap is all about. And it's a 40 dollar hat. Is this even going to sell? Isn't the joke from the mini-show that the hat and tee are so silly & wierd that only Big the Cat would ever wear them? Even though it is explained, the whole situation remains strange. And Green. This is a 2019 item.