Meek had his first head coaching experience at age 22, with the Fort Benning Doughboy football club in 1944, while serving in the Army during World War II.

[5] In 1951, Meek was offered his first collegiate head coaching position at Kansas State University with an initial salary of $8,000.

[5] Meek was offered the job even though he told the hiring committee at Kansas State that the program was in disarray.

When he learned after the season that an ineligible player had participated, he self-reported the violation to the NCAA, and the school voluntarily forfeited the win and the tie.

Meek accepted the services of several former Army players who resigned from the academy after violating the honor code in 1951.

The following year was even better, with Kansas State posting a 7–3 record and playing for an Orange Bowl berth in their final game (they went on to lose at Colorado).

Meek left Kansas State following the 1954 season, when the school refused to give raises to his assistants.

From 1962 to 1967, Meek worked as an assistant coach, including stints as Director of Pro Personnel for the Denver Broncos and as a scout for the Dallas Cowboys.