I think the Browning design takes the biscuit, but if you want to play the "is based on" game, the current Japanese-manufactured Weatherby XXII .22 autos are based on a Beretta design (the earliest ones were made by Beretta), which was based on a Walther design, which I believe came out right before WWI, although most of them are post-WWI.
But I don't have any specific dates, so the Browning still seems the surest winner. Interesting question.