Cooke enlisted in the Navy's Aviation Cadet Training Program located on the University of North Carolina at Chapel Hill campus in 1943. Cooke was stunned that one of the first recruits he met upon his arrival in the dormitory was Ted Williams, the American League batting champion. Cooke did not complete aviation training and instead spent the war as a Navy pharmacist's mate, 3rd class. During the war, Cooke participated in the Iwo Jima where his ship was attacked for more than three hours by Kamikaze, and then several months later in the Battle of Okinawa.