Westerns are fun to watch until you realize they are full of inaccuracies. Most Civil War movies show troops using Springfield Trapdoors or Winchester lever guns being carried in Indian Wars era.
It carries over to WWII. Early Pacific combat using M1 Garands, M1 carbines, etc.
If they are US Army troops, then they DID have M1 Garands!
The US Army had fully changed over by late 1941, with all of the Army active units in Nov 1941 having Garands.
Newly called-up Reserve or National Guard units still had 1903s, and some new Army units were issued 1903s pending manufacture & issue of more Garands, but the Garand was certainly present in numbers from the start of the US involvement.
It was the USMC that had resisted giving up their Springfields... it was watching (and using borrowed) Army Garands on Guadalcanal that convinced the Marines (both rank & file, but also senior officers... like Gen. Vandegrift) that the Garand was a better battle rifle.
The M1 carbine is another matter - it depends on when & where they are supposed to be. The first M1 carbines were delivered in mid-1942, with initial priority given to troops in the European Theater of Operations (ETO).