It's an old hat - maybe in the '20s or before - the crinkled leather brim is a giveaway.
The "P" button is generic & can be a hotel or restaurant.
The "Conductor" badge is generic as well. There may be a hallmark stamped on the reverse - if it is so much the better, if not - even more generic.
The hat badge & button may not be original to the hat.
Given the Chicago hat manufacturer - it is midwest origin since at that time, you bought your hats locally, more or less.
The shape is not a railroad hat, more like a doorman.
I could and have been wrong before, but hopefully, you have some information.
If you can't dazzle them with brilliance -
Baffle 'em with bulls**t...