The law will oblige either of the two sides to carry the burden of proof. Either Amazon has to proof the package was delivered, or the customer has to proof it wasn't. If the other sides does not accept the proof received, it has to sue.
Update: I should be clear, the shipper can prove it. The customer themselves can't without the shipper's acquiescence.
The shipper might be able to prove that the transport company picked up a package. Beyond that it's all hearsay if we are talking about fraudulent sellers.
The transport company might have evidence of a tracking number and thus most probably an actual package making it through the system. Shipments do get lost or stolen though. No way to prove anything really.
The customer can't prove it either. There are enough cases of packages with a tracking number having arrived at my and other people's doorsteps without the tracking ever showing that it happened. Why wouldn't the opposite be true? Driver just needs to scan package arrival not actually deliver. Of course there can be repercussions and I'd gather it's easier for a package to be stolen off other parts of the delivery chain. Anyway in this case both the shipper and customer have 'proof' / no proof to various degrees and in reality something 'fell off the truck'.
It's all about being convincing enough to whoever will be adjudicating this but 100% proof is impossible. The closest the customer could get I think would be 24h Video surveillance of their front entrance. No motion detection, just 24h continuous tape.