Since this is in alternatives to Mac hardware. You'll have to see if there is some serial number translator for whatever brand you are interested in.
Other than that manufacturers typically switch up models frequently. So, if you look up the full model number. You'll likely know about when it was built. At least within 6 months to a year depending on the model.
I'd be more worried about the physical condition of the laptop, battery health and the laptop's specs than the actual age. Those are far more important indicators of whether or not it'll be reliable and meet your needs.