Final answer:
Stax Records is the Memphis record label most closely associated with the birth of Soul music, contributing significantly to its development in the 1960s.
Step-by-step explanation:
The Memphis record label associated with the birth of Soul is Stax Records. This legendary label played a pivotal role in the development and popularization of soul music in the 1960s.
Although Elvis Presley, famously associated with Memphis' Sun Records, helped blend various regional music styles contributing to the creation of rock n' roll, it was Stax Records that was responsible for fostering the distinct sound of soul music with artists like Otis Redding, Isaac Hayes, and the Staple Singers. Presley's influence in blending gospel, blues, and country was significant, but when it comes to soul music specifically, Stax Records takes center stage.