While most people know of a football union suit, it actually got its name from one piece underwear popular between 1850 and 1920. Lastik Krotch made knee length union suit athletic underwear in the early 1900's. From what I can tell, the Lastik Krotch, and your box, were made between 1915 and 1920. It was marketed to athletes of all sports. The add below is from 1916.
www.antiquefootball.com