The German Bundesliga was founded in 1963 and Eintracht was part of the clubs that were in it from the start, up until their first relegation.
The 16 teams in the inaugural Bundesliga at a glance:
From Oberliga North: Hamburger SV, Werder Bremen, Eintracht Braunschweig
From Oberliga West: FC Schalke 04, Borussia Dortmund, 1. FC Köln, Meidericher SV, SC Preußen Münster
From Oberliga Southwest: 1. FC Saarbrücken, 1. FC Kaiserslautern
From Oberliga South: 1. FC Nürnberg, Eintracht Frankfurt, Karlsruher SC, TSV 1860 München, VfB Stuttgart
From Stadtliga Berlin: Hertha BSC
The first matchday kicked off on 24th of August 1963.
More info on Bundesliga and its history klick here