You can't. That is why some people are still Christians.
You can prove a negative- like if I say there is an apple in the box, and you want to disprove this i.e. prove that there is no such apple , all you have to do is look in the box- and if there is none- you just proved a negative.
The reason why we always prefer to look for proof of a phenomenon rather than absence is that most often its easier- like instead of the box if I said world and instead of apple if I said yeti- to prove that one exists all you have to do is find one but to disprove you have to look everywhere in the world- tough but still theoretically possible. So most often we make logical presumptions about such questions and most rational people would agree that its highly unlikely that a yetti exists.
In the case of God- the reason why existence cannot be proven/disproven is because no one to date has actually defined what God is. What are we supposed to look for or prove the absence of- even most ardent believer cannot precisely define God. So they generally descend into vagueness and abstraction- so I think the question really becomes how can you prove that God doesn't exist when no one really knows what God is supposed to be really.
Also in most cases the burden of proof should be on the one who proposes the existence- if you proclaim something to be true you should have rational material proof- and not wait around saying ok this is what I came up with now prove me wrong- if the world worked that way- the most successful people would be those who came up with the most outlandish theories and who refused to listen to any rational logic- no progress would ever be made.
The Paradox of Negative Information prevents proving a negative. If someone says there is an apple in a box and the box is opened and there is no apple in the box, that person has only failed to prove there is an apple in the box.
It's easier to prove something exists than to prove something doesn't because it's impossible to prove that something doesn't exist. If you fail to prove a thing doesn't exist, you only
failed to prove it. How can you provide evidence of the absence of something? You can prove, but you cannot not prove. <--
see the double negative?
Most people do not understand what dark matter or dark energy are, only a few people really do understand, but both have been proven mathematically.
Even though a full definition of God has not been given, people are able to prove parts of God. Rewording the question does nothing but avoid the issue.
And, if the burden of proof rests on the proposor, the detractors have nothing to say. How can anyone refute something they don't believe in? It is belief. Just like someone who believes in God cannot prove to someone that God exists. It is a matter of belief.