Okay, well, that’s slightly hyperbolic. The literal term “Air Cav”, according to the OED, dates from the mid-60’s. But the longer “air cavalry”, actually has a reference as early as 1913. Which, for extra fun times, contains the phrase “especially the aeroplanists at Nancy”.
air cavalry, n.
Mil. (chiefly U.S.).
A highly mobile division of an army which uses aircraft for a variety of functions, as observation, delivery of supplies and troops, aerial assault, evacuation, etc.