I did some digging and the only other piece of memorabilia with this particular batman image is from this 1966 Batman - The Caped Crusader poster on Etsy.
Some good info about the artist came from that listing:
Could this t shirt, in fact, pre-date the Adam West Batman movie of 1966 and be a comic book promo t shirt?This is a RARE VINTAGE ORIGINAL 1966 BATMAN THE CAPED CRUSADER POSTER, it's VERY BIG, and it features the artwork of long-time silver age Batman and Brave and the Bold artist CARMINE INFANTINO. This 1960's Dark Knight detective poster was produced by a company called G&F Posters of New York City (NYC), who also produced 1966 posters of Superman and Robin the Boy Wonder.
Here's an Infantino Pinup Batman #181 (June, 1966) So if this truly is one of the oldest known Batman t shirts around the real question is....what's it worth?