You can prove a negative. You can define something and then prove it doesn't exist. You can establish the premises of the argument and then construct a mathematical proof that it is logically impossible for something to exist. Wrt the Christian God it is not very difficult.
The simplest example rests on the empirical observation that evil exists, and the Christian definition of God.
Evil exists.
God is wholly good.
God is omniscient.
God is omnipotent.
Evil cannot exist if God is wholly good, knows about evil and has the power to stop evil. Evil does exist therefore God cannot exist.
Or
Nothing can come from nothing.
Evil exists.
Therefore if God is the Creator of all things he/she must be partly evil.
Therefore God as the defined Christian God does not exist.
So you can always say: yes but I don't accept that evil exists, or you could say, yes but I believe if a different God than the Christian God. But under certain established premises and definitions it's possible to prove a negative.
However I am a Christian, and a Christian can sweep aside such finicky nonsense!
Another essential element of Christianity is faith, as everyone knows. It's central. You cannot "have faith" in something that can be proved. You can't "believe" in something you've seen and experienced empirically. Therefore it's an essential element of Christianity that what you have faith in is difficult to believe, impossible to prove and easy to deny. Phew for us.
On top of that, we can say that humans don't understand the divine purpose of things that appear to be evil: and that our lives and suffering here on earth are a small and insignificant part of our eternal existence.
And on top of that, we can say that with God, anything is possible: that maths can prove that God does not exist, but the existence of maths proves that He does. (I like this one a LOT!)
So basically, it doesn't matter if you can prove it or not 
I should think very many if not most Christians are aware of the disproofs of God. So, there's no telling us. Even if you speak very slowly and treat us like very stupid children and even
sneer and poke fun. After all we wuz thrown to tigers once.