You cant prove it. Replace
From the looks of it it is already a scratched and old hob at the end of its lifespan. Glass hobs weaken with age, Replace and move on. you have had its use out of it.
Replace with Beko or B&Q, Currys etc. Not top line brand , no need.
Watch for similar scratches appearing soon after replacement with a new one - could indicate heavy pans and abuse. Take photo of this one to compare in future.
Impossible to prove - most likely something dropped on it but cracks can also happen if not installed properly.
Give them instructions on use - start at low temperatures and only gradually turn up. Never try to clean (esp not with cold water!) till cooled down totally. Be careful with heavy pans. Treat it as if it was their own - you will take their word this time but you have investigated and these hobs very rarely crack from normal use so if it happens again you will treat it as damage and they will need to pay for the replacement.
Replace it
Good luck
You have revealed their name, I would delete this if I were you