I concur that the cap is a fake. I would date it mid to late 70's though. The interior lining is not what one would expect in a period hat. The sports organization eagle makes no sense. The quality of the material used for the hat itself is not of either a style or quality one would expect to find on a period hat. The white piping glows even without a blacklight. Finally, Hitler never wore a hat in this color & insignia combination with the brown tunic, which of course is prewar. All you can say about this piece is the price was right.
Bob


"A man needs to know his limitations" Dirty Harry
Gold Badge #263