Wow!
I love this hat.
Check out this circa 1950's children's Baseball cap featuring the names of all the National League teams, at the time. It also includes game-action graphics, a flat red brim, and a red squatchee on top. (eBay auction link)
I have no idea where this vintage headdress comes from, but I'd imagine it's from a comic, candy or gum giveaway. Heck, maybe it's a prize you could've won at a carnival. I dunno.
All I do know is that apparel like this was uncommon for the era. Teams did not market to fans the same way they do today.