Not to take anything away from the brilliant guitarist Hank Garland, but Scotty Moore did most of Elvis' 50's hits. Garland didn't work with Elvis until he came back from the service in 1960 on "Elvis Is Back". Even then, Scotty is also credited on that album.
Hi, Thanks for reading, and thanks for writing in. FWIW, Wiki dates the Hank Garland/Elvis collaborations from 1958:
Garland is perhaps best known for his Nashville studio work with Elvis Presley from 1958 to 1961 which produced such rock hits as: "I Need Your Love Tonight", "A Big Hunk o' Love", " I'm Coming Home", "I Got Stung", "A Fool Such As I", "Stuck on You", "Little Sister", "(Marie's The Name) His Latest Flame", and "I Feel So Bad".