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