The falcons were founded in 1966 and have never won a Super Bowl.
While the Cardinals, Lions, Titans, Chargers, Browns, Bills and Vikings are older and have never won a Super Bowl, all won at least one AFL or NFL title before the 1970 AFL-NFL merger.
Congrats Falcons!
It’s actually a lot less time than you think when you consider that Brady was active for a little over 40% of the last 50 years.