Restoring `System.keychain` from a Time Machine backup without access to system `/var/db/SystemKey`
Solution 1:
Yes, unfortunately for all practical purposes the keys are gone for good.
You need the SystemKey file corresponding to that System.keychain in order to restore anything from it. If you haven't got a backup, you'll have to resort to bruteforcing the contents of the SystemKey file - which is not practically possible.