Oldest offenses still in use are the single wing and T(not the wing T, full house backfield). T formation might be the oldest formation in football. The single wing is less old, but single wing teams now have more in common with the single wing teams of the distant past than T teams do with their ancestors.
The wing T is a synchronizing of the two. Single wing plays from an under center look with T backs. Goes a lot deeper than just that aspect of course.
Funny enough the Double Wing is pretty modern, despite looking the most archaic to me. It’s creator only died in 2018. Important to note I’m speaking of the double wing offense, not just a double wing formation. Double wings have been used for a long long time.