You cannot prove that something not exist. In order to prove something inexistence you have to look every where in the world and check it. Even that is not enough because that could be outside of world too. 

However, there could be proofs for existence. There could be questioning and connecting dots and deducing a result from all. 

Meaning of existence is not physical thing and you cannot use this path. There are things we do not see, but we know that they exist. Even you could explain this like technology. There are some living microorganisms seen vis microscope. Think about there is no microscope and technology is not in the level of today. How could you prove there is microorganisms?

In my opinion there is no way to prove inexistence.