Must see some pics to further help on your M1
Like others posted, some pics, even quicky cell phone pics of key areas are needed to help really identify or value estimate for you.
By posting RRAD you have confirmed that your M1 is a US Army Depot level overhaul, done by US Army Armorers while on active duty.
The US Army Depot level overhaul program for M1 Garands was discontinued in early 1967 because the Depots began the overhaul program for M-14 rifles that had replaced the M1 Garand officially in 1957.
The Red River Army Depot in Texarkana, TX was very active in assembling very high quality M1 Garand overhauls to National Match standards and many of the last ones (1965/1966) went directly to government storage and are sometimes found in a "unfired" since test rebuild condition.
If your stock is VERY TIGHT fit to the receiver (i.e. do you need a trigger guard breaker tool to release the trigger guard from the stock?) AND if your "Box P" proof mark on the pistol grip looks like the pic below, then you definitely have a Red River Army Depot overhaul stock as this was their "proof" mark for the stock. Note that the "box" is really only 3 sides, not 4.
You can see the markings on op rod, barrel dates and proofs, and most important will be the RRAD overhaul date which should show on the receiver leg similar to mine pictured below from January 1966, using a brand new barrel from Springfield Armory, dated August 1965. Hooded rear sight, front sight are NM (National Match) and yours may be too.
Bottom line is that yes the serial number may place your M1 stripped receiver in the WWII era, the barrel date may be different manufacturer and date era, and definitely the rifle was through the Red River Army Depot as some point in its life.