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Burcham was born in Cadiz, Indiana, and grew up in Whittier, California in the eastern Los Angeles basin. Burcham sold burglar alarms of his own design to finance flying lessons from the O'Donnell School of Aviation in Long Beach, California, where he became chief instructor. In 1933, Burcham and Lt. Tito Falconi of the Italian Air Service competed in setting inverted flight endurance records. Burcham's flight of 4 h 5 min 22 s that December was not broken until July 24, 1991 when U.S. airshow pilot Joann Osterud set a new world's record of 4 h 38 min 10 s. In 1936, Burcham flew his Boeing 100 to the World's Aerobatic Championship at the National Air Races in Los Angeles.
In 1941, Burcham joined Lockheed as a production test pilot and spent a year as chief pilot of Lockheed's operations in England. He became chief engineering test pilot a few years later, and in that capacity was served as copilot on the first flight of the Constellation on January 8, 1943. On January 9, 1944, he turned the first flight of Lulu-Belle, the XP-80 prototype, into a thrilling low-level airshow before a crowd of military and civilian VIPs at Muroc Army Air Base (now Edwards AFB).