Possible dating of a Remington model 721 bolt action rifle in 30-06

[Casselman1961]

I acquired from my father which he got from his father. A early Remington model 721 bolt action rifle in 30-06 caliber and was hoping for some information to try to date it as close as possible. The serial number is 273703 and is located on the inside of the action (bolt) and on left barrel. I can't find any "letter" code on the barrel, there are numbers.

I attached pics, possible these pics can give an idea of the age.

Any help would be appreciated. I'm very curious on the age of this gun.
Its more of a "Hand me Down from family" type of pride thing.

Thanks for any help.

Bret