You may be able to locate a list of products you purchased through Apple where
a history, a warranty or AppleCare would have applied, from a page such as this:
https://getsupport.apple.com/
There is a link within the page, to view products, it asks you to Sign In with AppleID.
Although I'd previously been able to find a page of all my purchased items without
a separate login (while visiting ASC and already signed in) I don't see it now.
https://supportprofile.apple.com/
Hopefully you can either find old packing materials (box has barcode & serial number)
or paper trail from the date of purchase that also has the serial number.
Sorry to not be of much help...! 😐