Proving the Christian God to be false is simple. His properties are known to us. The Bible says that God created the universe 6-12k years ago. This is false. We know from radiometric dating, from the distance of stars and the amount of distance their light has to travel to reach the Earth, and the rate of expansion of the universe that the Earth is billions of years old. The Bible says the Christian God created men from mere dust and women from man's rib, and created all the animals in one day, and we know this is not true, either. Animals and humans emerged from a gradual process of genetic mutations and adaptations, mate selection, etc., commonly known as evolution. A lot of Christians don't believe this, but it's a scientific fact. Some choose not to accept this, but that has no bearing on whatsoever on it being true. The Bible also says disease is caused by demonic possession. Now we know and accept the existence of viruses and bacteria. The Bible also says that the Christian God is personally responsible for rain and earthquakes, but we now know about evaporation and have discovered plate tectonics. The Christian God says the Earth is flat, and now we know it is round. Apparently, the Christian God didn't know any of this, despite creating the universe and supposedly being "all-knowing". His knowledge was limited to the humans of his day. Coincidence?
No atheist can disprove a God whose properties are unknown to man, however. It's an unfalsifiable hypothesis. No matter how much evidence you find that contradicts the existence of said God, believers can always come up with an excuse. If we searched every square inch of the entire universe and found no God, believers could say, "Maybe he's invisible, or maybe he exists in an alternate dimension."
I own an invisible tyrannosaurus-rex. And it cannot be touched. It's invisible, and it's ethereal, but I own it. Do you believe me? Probably not. Can you prove that I don't own it? No, you can't. It's an unfalsifiable hypothesis. I can make any number of unfalsifiable hypotheses, and you can't disprove any of them. Nobody can. That's the beauty of your argument. Nobody can disprove your theory, and then you turn around and say, "See! It can't be disproven, therefore, it must be true!" Just because your theory cannot be disproven, that doesn't mean it's true.