The only way to definitively prove something does not exist is to observe, with 100% accuacy, the entire universe at every scale at the same time. If it's not there, it logically doesn't exist, ignoring the possibility of it popping in and out of existence. I'm purposefully ignoring things like "what if it exists outside of our universe" because that would, for all intents and purposes, have no effect on us.
But in this case, proving something doesn't exist is needless. The burden of proof rests with the person who made the assertion "X does exist". If they can't prove it, their statement is considered false. And saying "well you can't disprove it" is in no way proof. By that particular reasoning, I could "prove" literally anything. E.G., "all humans have a finite chance of randomly transmuting into a strawberry popsicle. But they cannot ever change into a raspberry popsicle", "somewhere in the universe, at any given point in time, there is an army of mutant robot zombie Hitler ninja communist hacker Pokemon devouring the very fabric of space time". Neither of those can be disproved, because a "finite chance" could be one in unthinkable powers of ten, and I dare you to scour every point of space in the universe simultaneously.