Their first gig was opening up for a lineup of Iron Butterfly that a friend was in.
From the article above:
One of the first heavy rock bands, Iron Butterfly were formed in San Diego in 1966. It is fitting that there should be strong links between the Tap and Iron Butterfly, for whom the description "heavy metal" is believed to have been coined. The band plotted a similar course to the Tap, moving from psychedelia to heavy rock and pushing the envelope of the four-minute pop song to the epic form with their classic In-A-Gadda-Da-Vida (the album of the same name is said to have sold 25m copies). Spinal Tap played their first live gig at Gazzari's on Sunset Strip, in a double bill with Iron Butterfly."
This is another interesting point from the article that I hadn't previously considered:
"Last Waltz, The
Directed by Martin Scorsese, one of the inspirations for Martin DiBergi, this proto-rockumentary records the last performance by The Band, which Robbie Robertson describes as "the beginning of the end of the beginning".
The interview technique of This Is Spinal Tap is lifted straight from The Last Waltz, where Scorsese placed himself in front of the camera for some of his chats with the band, of which he was a declared fan. In the interviews, the band explain that they got together having been assured that they would get "more pussy than Frank Sinatra".
Among the film's Tap-like moments: the band members discuss the pleasures and pains of 16 years on the road, and the tensions and joys created by mixing music and women; a very obviously and chronically goofed keyboardist, Richard Manuel, recalls the band's problems with settling on a name: "It was right in the middle of the whole psychedelia, Chocolate Strawberries and Marshmallow Overcoat - those kind of names. They were the Hawks and toyed with becoming the Crackers or the Honkies before eventually settling on the Band." In a very Tap-like observation, Robbie Robertson acknowledges what rock'n'roll had done for them: "It took us everywhere. It took us to some strange places... physically, spiritually and psychotically."