Exactly what the title says. The leveled list LL_Armor_Forged_Helmets (0013105A) contains Armor_BoS_Field_Scribe_Helmet, which is explicitly Brotherhood of Steel equipment. This makes it the first place you can encounter the hat, because it is available via the Forged at Saugus Ironworks from the very start of the game, even before the Prydwen shows up in the Commonwealth.
This leveled list has already been edited by the Unofficial Patch in order to remove another piece of equipment that was full armor rather than just a helmet, and I suspect this hat was added by mistake as well. The common theme for this list is goggles and hard hats, with every item in it having one or the other with little regard for other things such as where the item came from or how much of the body it covered.