Born in Indianapolis, Indiana, Finch's family moved to Hialeah, Florida, when he was an infant. His favorite group growing up was The Beatles. His musical tastes grew to include soul and country and western music. In his early teens, Finch got his first electric bass guitar and began to learn country music bass lines. He joined several country bands before joining the band Ball & Chain.
Finch became interested in audio recording techniques and a schoolmate introduced him to the singer-songwriter Clarence Reid from TK Records. His high school attendance suffered as he spent every free moment at TK Records and eventually was hired as a part-time recording engineer for the label. Henry Stone and Clarence Reid introduced him to Harry Wayne Casey, three years his senior, who worked in the shipping department. Prior to his introduction to Casey, Finch had already established himself at TK as a skilled engineer, with over 127 singles recorded before the age of 17 (including various tracks for the Allman Brothers and Mother’s Finest).
Within weeks of meeting, the Finch/Casey songwriting collaboration began, with their first hit songs recorded by Betty Wright and George McCrae ("Where Is the Love" and "Rock Your Baby"). Finch then assembled the future Sunshine Band members, utilizing his already-established friendships with TK session musicians, guitarist Jerome Smith and drummer Robert Johnson. The Finch/Casey collaboration produced numerous hits, including, "(Shake, Shake, Shake) Shake Your Booty", "Get Down Tonight", "Please Don't Go", "Boogie Shoes" and "I'm Your Boogie Man".