Operations Research is a somewhat eclectic term. The British coined and promoted it, so in the early stages they were the only ones using it even if others were doing similar things under different names, before and after. On the US military uses there is a comprehensive monograph, History of Operations Research in the United States Army by Schrader (freely available), in three volumes. Schrader uses a substantive description rather than the name to trace pre-history of Operations Research all the way back to the Napoleon wars. Here are some excerpts:
"The starting date for this study, 1942, was determined by the first efforts to create an OR capability in the U.S. Army; the ending date, 1962, was determined by the beginning of the major changes in Army organization and procedures instituted by Secretary of Defense Robert S. McNamara, notably the initiation of efforts to reorganize the Army along functional lines and to consolidate related activities under major functional commands, such as the U.S. Army Combat Developments Command and the U.S.
Army Materiel Command... Between 1942 and 1962, the main thrust of OR work in the U.S. Army was in fact the improvement of weapons and equipment, organiza-
tion, tactical doctrine, and, to a lesser degree, the formulation of higher-level strategy and policy pertaining to the political, economic, and social issues facing the Army."
[...] The United States Navy owns the distinction of having the fi rst active OR group in the U.S. armed forces: the Mine Warfare Operations Research Group (MWORG), established informally in January 1942.
The Navy’s early adoption of OR was partly the result of prewar contacts with British OR groups at RAF Coastal Command and the Admiralty working on problems of naval mining, antisubmarine warfare, and convoy organization. The work being done in Britain was directly applicable to the problems faced by the U.S. Navy immediately after the Pearl Harbor attack... MWORG was officially established as part of the U.S. Navy Bureau of Ordnance’s Re
search Division on 24 June 1942, but it had existed informally since late January 1942 and thus merits distinction as the first OR organization in the U.S. armed forces.
MWORG grew out of work being done on countermeasures for German magnetic mines from December 1939 at the Naval Ordnance Laboratory (NOL) in Washington, D.C. The NOL Mine Research Unit, led from early 1940 by Ellis A. Johnson, a Carnegie Institution physicist, focused on techniques for sweeping for magnetic mines and degaussing (demagnetizing) U.S. naval and merchant vessels. In July 1940, Ralph D. Bennett, a professor of electrical engineering at MIT, was called to active duty as a lieutenant commander, U.S. Naval Reserve (USNR) and was assigned the task of expanding NOL staff, which he did by bringing in accomplished scientists of his acquaintance, increasing the scientific staff at NOL from a dozen to nearly one thousand."
Starting in 1942 Army air, ground and service forces joined the Navy.