Melia joined the Reds straight from St. Anthony's School as a 15-year-old, when manager Don Welsh saw the potential in the young schoolboy international's feet, Melia signed professional forms on his 17th birthday, 1 November 1954. After 23 appearances for Liverpool's reserve team, Melia made his début aged 18 on 17 December 1955 at Anfield in a 2nd Division fixture against Nottingham Forest. The visitors came up against an in form Billy Liddell who scored a hat-trick in the 5–2 victory, Jimmy also scored his first goal for the club in the 48th minute, John Evans got the other.