Cresswell started playing for Bridlington Rangers at the age of eight before joining the York City youth system aged 14 in 1991. Having been top scorer for the Northern Intermediate League team for three consecutive seasons, he signed a professional contract on 15 November 1995. Cresswell made his first-team debut away to Brentford in a 2–0 defeat in the Second Division on 20 January 1996. He first scored for York with the second goal of a 2–2 draw away to Bradford City on 2 March 1996. This proved to be his only goal in the 1995–96 season, in which he made 17 appearances.