Letterman's First Tonight Show Appearances
It looks like the first time David Letterman was ever on The Tonight Show (as a guest) might have been November 24, 1978. His first time as guest-host might have been less than two months later on January 22, 1979.
If correct, that seems like an awfully short period of time to go from a guest to guest-host. Carson seemed to have recognized Letterman's skill as a late-night host right away.
It'd be great if, at some point, they rerun those two shows on Antenna.