The birth of the printed t-shirt apparently dates back to the early days of WWII:
The existence of the t-shirt dates way back to the 1890s as an undergarment. However it was not until 1942 that t-shirts became appropriate to wear on their own and even get something to say on them. This Air Corps Gunnery School t-shirt featured on the cover of LIFE magazine of July 13, 1942, is believed by many to be the first printed t-shirt ever worn publicly.