New IPhone back side cracked

Unless it was cracked before you opened the box (meaning you haven’t been using it and then it cracked somehow) then they wouldn’t change it. You would have to pay to have it repaired/replaced. Either through AppleCare+ for the reduced cost or whatever the full repair/replace cost would be. Are you trying to say it was cracked as soon as you got it out of the box?

My iPhone 12 mini developed a small chip/crack in the back glass in the first week even though I didn't drop it or do anything that would have caused the damage. I really hope this isn't a sign this phone is not as durable as my previous iPhones.

The rear glass can not be repaired and the device must be replaced.