Young was born in Fallowfield, Manchester, where he lived with his parents and older brother Chris. His house was half a mile from Manchester City's Maine Road ground, which was visible from the bedroom window. As a schoolboy he played for Manchester Boys, facing opponents who were two years older. After catching the eye of scout Harry Godwin, Young signed for Manchester City as an apprentice in 1959, turning down the opportunity to join Manchester United. Around this time he was capped by England at youth level. He turned professional in July 1960, and made his first team debut in November 1961, in a 2–1 defeat against Aston Villa at Villa Park. After breaking into the team for the first time, Young played every match in the remainder of the 1961–62 season. He scored his first goal for the club on 23 December 1961, in a 3–0 home win against Ipswich Town. He finished his first season with 11 goals in 26 appearances.