Born in a suburb of Aarhus, Tøfting started playing at local club ASA in the borough of Frederiksbjerg before joining the largest club in the city, Aarhus Gymnastikforening (AGF) at age 10 – a club he would frequently return to during his career. He made his senior debut for the club on 29 October 1989, in the 1–0 victory against Aalborg BK. He won the 1992 Danish Cup with the team, and made his debut for the Danish national football team in January 1993.