As much as I am rooting for this cap to be something special, I suspect it's an amateur or youth cap from the 1950s or 1960s, based on the thin leather band, course material and elastic back.
As a cap collector, I constantly struggle to identify what I have. It seems to me that without a good photo match, it's just speculation. For this one, that would require finding a photo of a lighter colored cap being used by the Newark Dodgers, and dating its various details to how caps were made in the mid-1930s.
I bought a bunch of caps from a major Ebay seller a few years ago, and he gave a precise description for every cap. Nearly all were way off, including a "1960s Japanese cap," which turned out to be a 1938 Boston Bees game cap. Some people just make stuff up, including several major sellers. I do believe it's on the seller to back up any claim they make about an item, if their are any doubts about it being true.
This site is the most useful one I've found when it comes to dating caps. It's just MLB caps, but there are a lot of good images of caps from the 1930s for comparison ...
https://mlbcollectors.com/MLBcapindex.php