Nike, a consistent innovator in athletic and sports products, was founded in 1960s.
However, its first patent, US4183156A, claims a priority of Jan 14, 1977, and appears to be covering Nike's Air technology invented by M. Frank Rudy.
Frank Rudy, who was an aerospace engineer, went to many shoe companies with his invention. However, he was turned down. His invention required complete rehaul of the way shoes were made back then; Not many companies were willing to risk changing the present.
Nike did.
More on Air sole shoes from Nike, here