Cobb is the daughter of Lt. Col. William H. Cobb and Helena Butler Stone Cobb. As a child growing up in Oklahoma, Cobb took to aviation at an early age, with her pilot father's encouragement. Cobb first flew in an aircraft at age twelve, in her father's open cockpit 1936 Waco biplane. At 16, she was barnstorming around the Great Plains in a Piper J-3 Cub, dropping leaflets over little towns announcing the arrival of circuses. Sleeping under the Cub's wing at night helped scrape together money for fuel to practice her flying by giving rides. By the age of 17, while a student at Oklahoma City Classen High School, Cobb had earned her private pilot's license. She received her commercial pilots license a year later. In 1948, Cobb attended Oklahoma College for Women for a year. By age 19, Cobb was teaching men to fly. At 21, she was delivering military fighters and four-engine bombers to foreign Air Forces worldwide.
Facing sex discrimination and the return of many qualified male pilots after World War II, she had to take on less sought after jobs, such as patrolling pipelines and crop dusting. Nevertheless, she persisted. She went on to earn her Multi-Engine, Instrument, Flight Instructor, and Ground Instructor ratings as well as her Airline Transport license. Cobb went on to set new world records for speed, distance, and absolute altitude while still in her twenties. When she became the first woman to fly in the Paris Air Show, the world's largest air exposition, her fellow airmen named her Pilot of the Year and awarded her the Amelia Earhart Gold Medal of Achievement. Life Magazine named her one of the nine women of the "100 most important young people in the United States." To save the money to buy a surplus World War II Fairchild PT-23, and a chance to be self-employed, Cobb played women's softball on a semi-professional team, the Oklahoma City Queens. Due to the return of many qualified male pilots after World War II, Cobb had to take on less sought-after jobs, such as patrolling pipelines and crop dusting. She went on to earn her Multi-Engine, Instrument, Flight Instructor, and Ground Instructor ratings as well as her Airline Transport license. In 1953, she was employed by Fleetway, Inc., ferrying war surplus aircraft to various air forces and civilian aircraft enterprises, including to the Peruvian Air Force. At a fueling stop in Ecuador, she was arrested for suspected espionage. After two years, Cobb returned to the United States and became a pilot and manager for the Aero Design and Engineering Company, which made the Aero Commander aircraft she used in setting her three world aviation records: the 1959 world record for nonstop long-distance flight, the 1959 world light-plane speed record, and a 1960 world altitude record for lightweight aircraft of 37,010 feet. She was one of the few women executives in aviation and was also the first woman to fly in the Paris Air Show. In addition to these aviation accomplishments, Cobb was one of the thirteen Fellow Lady Astronaut Trainees (FLATS) (also referred to as the Mercury 13), who underwent the same physical tests as the original Mercury astronauts. She went through NASA's rigorous testing program and passed all the training exercises, ranking in the top two percent of all astronaut candidates. In May 1961, NASA Administrator James Webb appointed Cobb as a consultant to the NASA space program for the future use of women as astronauts. However, she was unable to rally support in Congress for adding women to the astronaut program and so resigned from her position. Cobb then became a private pilot conducting humanitarian aid missions to the peoples of the Amazon rain forests in six South American nations, spending her time as a solo pilot delivering food, medicine and other aid to indigenous people while surveying new air routes to remote areas. Cobb has been honored by the Brazilian, Colombian, Ecuadorian, French, and Peruvian governments. Over her career Cobb received numerous aviation awards, including the 1959 National Pilot's Association Pilot of the Year; the Harmon International Trophy; the Amelia Earhart Gold Medal of Achievement; the Bishop Wright Air Industry Award; and the Fédération Aéronautique Internationale's Gold Wings Award. Cobb published two autobiographies, Woman Into Space, and Solo Pilot. In 1999, Cobb was the subject of an unsuccessful National Organization for Women campaign to send her to space (like Senator John Glenn) to investigate the effects of aging. She continues her relief efforts for the peoples of the Amazon. By 1959 (age 28) she was a pilot and manager for Aero Design and Engineering Company, which also made the Aero Commander aircraft she used in her record making feats, and was one of the few women executives in aviation. By 1960, she had 7,000 hours of flying time and held 3 world aviation records: the 1959 world record for nonstop long-distance flight, the 1959 world light-plane speed record, and a 1960 world altitude record for lightweight aircraft of 37,010 ft. In May 1961, NASA Administrator James Webb appointed Cobb as a consultant to the NASA space program. Although she never flew in space, Cobb, along with twenty-four other women, underwent physical tests similar to those taken by the Mercury astronauts with the belief that she might become an astronaut trainee. All the women who participated in the program, known as First Lady Astronaut Trainees, were skilled pilots. Dr. Randy Lovelace, a NASA scientist who had conducted the official Mercury program physicals, administered the tests at his private clinic without official NASA sanction. Cobb passed all the training exercises, ranking in the top 2% of all astronaut candidates of both genders.