This is basic blue baseball cap purchased for £3 pounds
I then distressed to make it look well used for a post-apocalypse environment
Now there are lots of online videos teaching you how to distress items, from dragging behind cars to burying in the mud for 6 months.
But the easiest and quickest way is a mixture of spray paint and coarse sandpaper.
and then just rub in the dirt, possible while the paint is still wet.