This is a WW2 era rebuild of an earlier rifle using a replacement Springfield Armory barrel and a "scant grip" stock. Altho the M1903 was supplanted by the M1 Garand as the standard WW2 infantry rifle, M1903s were maintained in service thru WW2.
Replacement M1903 barrels were produced during WW2 by Springfield Armory into the latter half of 1944, Johnson Automatics, Remington, Sedgley (some marked U.S.M.C for separate USMC procurement) into early 1945, and High Standard into late 1944. I have owned M1903s fitted with all of these barrels, except Johnson Automatics, and they all shot well.
Replacement stocks which were installed during arsenal rebuilding were stamped with a "P" proofmark and the cartouche of the rebuild facility. Stocks which were replaced at unit/post/base level did not have these marks applied.
A Springfield Armory receiver numbered above 800,000 is classed as a "high number" receiver and is safe to shoot as a result of improved heat treatment at time of manufacture. "Low numbered" Springfield Armory receivers were taken out of service by US Army Ordnance policy following WW1 due to a number of documented incidents of receiver failure. That said, some low numbered receivers were kept in use during WW2, especially by the USMC which maintained separate supply channels. The consensus among collectors today is to not shoot a low numbered M1903.