Actually, Mbo, the song he recorded for his mother's birthday was a piece of syrupy drivel called "My Happiness". When he recorded "That's All Right, Mama" some months later, it was the result of a lot of trial and error in Sun Studios with Scotty and Bill, trying various songs in various arrangements and seeing if something worked. The moment itself is shrouded in legend, but the more persistent legend has it that Elvis started fooling around with the song during a break in their more "serious" efforts, Scotty and Bill jumped in, and then Sam Phillips (owner of the studio and recording engineer) told them to do it again while he ran the tape.