The hat is a non ridged soft Crusher Cap type of hat that a pilot would wear their headset over wile flying an aircraft. The Officers hat insignia is a "V-Wing" type of Eagle.
The Army had both the "V-Wing", and the "S-Wing" types during WW2. But, the "V-Wing" type of hat eagle was only used during WW2, and fell out of use after the war ended. There are no size markings in this hat. I have no idea what size it is, or even care what size it is.
It is for sale "As Is", as an old relic collectable only. It is not for sale as wearable clothing, or as a usable item. It is an old relic...