Answer:
Contrary to previous answer, police officers do not have a computer data base showing WHEN a gun was made. (Retired police officer here) In some cases, the manufacturer has records, or collectors have compiled records, showing the year a gun was made. Sometimes, this is easy to find- Remington marked rifle and shotgun barrels with a letter code that can be researched. Ruger and Browning have historical data available on their website. Marlin lever action rifles used a letter prefix to the SN. However, for many firearms, there is no historical data available- companies closed, records lost in disasters, etc. To complicate this, many rifles and shotguns never HAD a serial number- they were not required by US law until 1968. My collection includes 4 of the Remington 550-1 rifles- none of them have ever had a serial number.