Moore's early background was in jazz and country music. A fan of the guitarist Chet Atkins, Moore led a group called the Starlite Wranglers before Sam Phillips at Sun Records put him together with then-teenage Elvis Presley. The trio was completed with the bass player Bill Black, who brought a "rhythmic propulsion" that much pleased Phillips. In 1954, Moore and Black accompanied Elvis on what would become the first Presley hit, the Sun Studios session cut of "That's All Right", a recording regarded as a seminal event in rock and roll history.