Hickson started his football career as a teenager with non-league Ellesmere Port Town, where his robust style and keen eye for goal were noticed by the Everton manager Cliff Britton. He signed for the "Toffees" in 1948, but serving his stint of National Service delayed his debut for another three years. During this period he played for the Cheshire Army Cadets team, and it was with them that he was coached by the Everton legend Dixie Dean. It is fairly safe to assume that Dave developed the physical side of his game in this period. Hickson made his debut for Everton in September 1951 against Leeds United, with the Blues in Division Two for only the second season in their history. Hickson was soon a regular fixture in the Everton side.