There is no need for anyone to prove anything. As I’ve said at the onset:
Here’s what skeptic philosopher Austin Dacey says about proof being not necessary.
To conclude, have we proven a negative? Well, the word “prove” is tricky. Sometimes proving means offering reasons that establish a claim with certainty beyond any possibility of doubt or error. It would be nice if all questions could be resolved with this degree of certainty. But, in fact, almost nothing we can know, including our scientific knowledge, can be proved in this sense except in logic and mathematics perhaps.
So, proof is not the issue. The issue is what is the most reasonable explanation for the shroud. And as I’ve argued in my summary argument, the most rational explanation is it is the authentic burial shroud of Jesus.