Well, some of the old Kodak and most of the Fuji, even Ilford, do not have expiration dates on packaging of their papers. How do you know they are new or old?
Most paper is very slow something in the neighbourhood of ISO <5 so while film can expire in 2-3 years, for paper it's more then 10 years. If you went into the store and saw paper that expires in 2025, you would probably not believe it's correct. Most companies put an emulsion number on the box which includes a date code, if you call the companies customer service line or email them and give them the emulsion number, they can tell you, if it's old paper. Other hints, they usually update labels once in a while, so if you see an old style label, it's probably old paper. What I did, back when I had my DR up and running, I would buy a 100 sheet box of paper, split it into 25 sheet packages, one would go in the paper safe, the rest were put in light proof bags, then wrapped in foil, that was put in a plastic bag with a label, and dropped into the freezer. That was 1982 - I bet if I had one of those packages now, it would still be good.