He was the son of Jan "John" Souček, who had been born in Ovčáry, Bohemia (then part of Austria-Hungary, now in the Czech Republic), but had emigrated to the United States at the age of 7 with his family.

Soucek entered the United States Naval Academy in 1918 and served with the rank of midshipman aboard the battleship Missouri (BB-11) during World War I.

He was assigned to the Navy's first aircraft carrier Langley (CV-1) in November, and served as assistant flight officer of Observation Squadron 2.

In May 1927, he was assigned to the Naval Aircraft Factory in Philadelphia, before transferring to the Bureau of Aeronautics in July to serve in the Power Plant Design Section.

On June 4, 1930, Soucek flew an Apache landplane equipped with a 450 horsepower (340 kW) Pratt & Whitney R-1340 radial engine to a height of 43,166 feet (13,157 m) over Naval Air Station Anacostia, regaining the world record he had held in 1929.

Soucek was appointed executive officer in 1942, and served in that capacity during the Doolittle Raid on Tokyo on April 18 and during the Battle of the Santa Cruz Islands.

[2] Apollo's younger brother Zeus (1899–1967), also joined the Navy, became an aviator, and set speed, distance and duration records piloting a Naval Aircraft Factory PN-12 in May 1928.