1920 (no date code stamp)
1924, see related links.
January 6 1902-43,897 were made
Serial number 3273324 regards an early war (1941) built Remington Model 1903 Service Rifle, in caliber 30-06. Remington 1903A3 productions did not begin until 1942 dated to serial number 3348086 and higher.
1920 (pre date code) and maybe even Model 12 on the receiver?
Please check the link for the Manufacture Date codes details on the Remington Society of America.
Your Remington model 1903-A3 was made in the year 1942.It was chambered in the caliber 30-06.
You will have to contact Remington.