The M1903A3 was standardized May 21, 1942, the contract was awarded two weeks later. Remington continued M1903Modified production until March1943. Remington made 707,629 M1903A3 rifles. The contract was cancelled Feb 28, 1944.
The large number of M1903A3's saw service in both theaters of war2. I have my uncles photo's of 101st airborne troops in gliders on D day, many are carrying the M1903A3. There are many books in print that discuss the use of the 03A3 during the war and the misconception that it was not.
At the end of the war a large number of these were sent to ordnance facilities for inspection and overhaul prior to long term storage. Some of these were new but they may have received the ordnance stamp with no work done to the rifle.