Your quandary can be solved readily enough with a study of the Federal Census. Given the number of generations you cite, certainly one or more of those individuals was born 79+ years ago. As such, they will, in all likelihood, appear in the census. Once found, you simply need to continue back in time until you find a connection to a documented line.
Other records you might wish to consult are birth and death records. Those will only get you back to around 1900 — give or take a decade, but will permit you to generate a verifiable lineage from which to work.
Citing an experience in my own family to illustrate the point. For several generations, my GGgrandfather's name was believed to be Richard MAY. This perception stemmed from the fact that he was always referred to as "Dick". Turns out that, while "Dick" was his nickname, neither of his given names were Richard. In fact, his name was Drury G. MAY. Thus, one can never trust family lore alone. You must strive to locate verifiable primary source documentation.