Can you check the serial number like you can with Colt ?
Absolutely . The Cody Museum in Wyoming have all of the existing Winchester records. They will be able to tell you when the rifle was made, who it was shipped to as well as caliber, special order features and more.
Repeat story from earlier this week. They traced the serial markings on the tang to a manufacture date of 1882-83. That doesn’t mean the rifle has been sitting there since then; but it has been there for awhile.