Cobb graduated from the University of Georgia in 1937 with a degree in Landscape Architecture, He served as an engineering officer in the U.S. Marine Corps during World War II. He was assigned to construct a golf course at Marine Corps Base, Camp LeJeune, North Carolina, to serve as a physical rehabilitation facility. He worked with veteran architect Fred Findlay on the project. It is possible that this assignment developed his design philosophy that golf was supposed to heal and to stimulate, not punish.
In the mid-1950s, Cobb established an office in Greenville, South Carolina, and profited with the booming golf development climate with dozens of original designs, along with redesigns.
Perhaps his most known design is his shortest course: The Par 3 Course at Augusta National Golf Club, which he completed in 1959