De Wit made his debut for FC Utrecht in the 1982–83 season. He was a member of the Dutch squad at the 1983 FIFA World Youth Championship. He was transferred to Ajax Amsterdam two seasons later, July 1984, as successor of left wing attacker Jesper Olsen, who left to Manchester United. At Ajax, he quickly became a crowd favourite, and played nearly all of the matches, the 1984–1985 and 1985–1986 seasons. On 1985-05-01, still in his first season at Ajax, De Wit made his debut for the Dutch national team in a World Cup qualifier against Austria. Nearly two weeks later, De Wit scored the winning goal against Hungary (0–1 away win), which won the Netherlands a play-off match against Belgium for the 1986 FIFA World Cup.
