Hey look 15 shows and I saw zero of them. This is the master list of tunes the Grateful Dead opened a show with only once; I expect there are more in the 1965-1967 era but I could not tell you precisely.
The 15 songs below are the only songs that the Dead opened with exactly one time.
Obviously, Bo Diddley was played first and best with Bo Diddley himself. I never saw Loose Lucy as an opening song
Franklin's was a jack of all trades tune played everywhere in the show, especially at the start of its run.
Hey Bo Diddley 03-25-1972 first one
Loose Lucy 02-15-1973
Wave That Flag 02-21-1973
Crazy Fingers 06-17-1975 first one
Terrapin Station 02-26-1977 first one
Franklin's Tower 05-09-1978
Day Job 04-13-1984
Big Boy Pete 11-21-1985
Day Tripper 06-25-1985
Mighty Quinn 03-03-1987
Eyes of the World 06-17-1991
Salt Lake City 02-21-1995 first one
Here's a few of the tunes