Balme played his junior football with Wembley Athletic Club, after leaving Mount Pleasant Amateurs, before transferring to Western Australian Football League (WAFL) club Subiaco in 1968. Aged just 16, Balme created a huge impression with a strong performance in the ruck against future Australian Football Hall of Famer Graham "Polly" Farmer in a game against West Perth Football Club. In January 1969, he moved to Melbourne with his family. He was quickly enticed to sign with Richmond along with his older brother Ian Balme.