McGowan made his Celtic debut in the 5–0 win over Inverness Caledonian Thistle in September 2007, where he came on as a substitute. He scored his first senior goal for Celtic on 7 August 2008 in a pre-season friendly against Manchester City at Celtic Park. He had the chance to score his second senior goal to win the game for Celtic but his shot hit the crossbar and the game ended 1–1. McGowan made his Champions League debut against Villarreal on 10 December 2008, as a 75th-minute substitute for Aiden McGeady. Celtic won the match 2–0 but finished bottom of their group.
In the 2009–10 season, McGowan soon became part in the first team, under manager Tony Mowbray. On 17 December 2009, just over a year to the day of his European debut, McGowan made his Europa League debut in a 3–3 draw away to Rapid Vienna. He made an impact in the 91st minute by scoring his first competitive goal for the Hoops to complete a comeback from 3–0 down to draw 3–3. On 24 January 2010, McGowan made an impressive display when he provided double assist for Marc-Antoine Fortuné and Paddy McCourt, as Celtic made a comeback from 1–0 down to 4–1 up, against St Johnstone.