Unlikely. The easternmost stretch of Sunset Boulevard near downtown came into existence around 1910. Prior to that, that right-of-way was named Bellevue. So the low-digit addresses of Sunset have been in the L.A. city limits from the beginning.
However … there used to be addresses on Sunset lower than 1000. Sunset used to extend a little farther east than it currently does. That stretch of road has since been renamed Cesar Chavez Blvd.
But I don’t think you ever would have found a 77. Street numbers in L.A. are counted from Main Street downtown and as you can see from this map from 1917 Sunset didn’t quite make it to Main. If a number 77 did exist it would have been right at the very end of the street, just a few blocks from the L.A. City Hall.
And miles and miles away from the stretch of Sunset that would eventually exist run through Hollywood and be called the Strip.