If the theist of whatever religion wishes to prove the existence of their own god, then it is incumbent upon the theist of whatever religion, to rationally demonstrate both the non-existence of all rival gods, and the true existence of their own particular god. The Muslim must rationally demonstrate that Yahweh, Zeus, Odin, Brahma, etc., does not exist and that Allah does exist. The Christian must rationally demonstrate the non-existence of Allah, Zeus, Odin, Brahma, etc., and the true existence of the resurrected and glorified Christ.
The theist must rationally explain how they know their god or gods exist and all others are mythological beings. The theist must also present and explain what evidences he or she uses to arrive at their conclusions. The Bible cannot be used to prove the Bible's claims. The Quran cannot be used to prove the Quran's claims. Anecdotal accounts also do not prove the Bible's or the Quran's claims, nor the real existence of the books' respective gods.
To quote Carl Sagan: "Extraordinary claims require extraordinary evidence". Religious claims are quite extraordinary, and so the evidence proving those claims must likewise be extraordinary. The establishment as fact of the existence of any god must meet and satisfy all the same criteria used to establish all other verified truths.
The reason that science is our best way of getting at the truth is because all scientific theories are subjected to a variety of rigorous testing and observation, tests that produce the same results when conducted by any other scientists. Because of this science is falsifiable, and when new findings come to light and are established as facts, older theories are improved upon, revised, or rejected altogether.
A scientific theory, if it is to be established as fact, cannot conflict with or contradict any other established facts. That's why science knows that something is wrong somewhere with Newton's or Einstein's theories, and are continuing to do research into how to reconcile Quantum physics and Newtonian physics.
Sciences' rigid self-policing to find and correct errors makes science the best method to find the true way the universe works and the nature of reality. Scientists go where the evidence leads whether or not they like the results and possible repercussions. If overwhelming evidence came to light, meeting all the criteria for establishing a theory as fact through rigorous testing and peer review, establishing the true existence of some god or other, then all reputable, respectable, non-believing scientists will admit their mistake and accept the existence of some kind of God.
Is religion self-correcting ? Would any facts, however well established and proven, move a Christian to drop their belief that Jesus is a divine being or that he died as an efficacious sacrifice for sin and then raised to life again ? Would any fact move a Muslim to drop their belief in divinely inspired prophets ? Some Christians and Muslims have made the jump from religion to atheism, and continue to do so, as a result of following where the evidence leads, but many refuse to give up their religious beliefs even in the face of the most overwhelming contrary evidence. The result of the change is not due to any self-policing within religion, but only because individual believers decide on their own to really compare the beliefs of their religion with the facts of science. That brings to mind a poignant saying that seems to fit here: "Philosophy are questions that may never be answered, religion are answers that may never be questioned".
And then there is the matter of the burden of proof. The non-believer in Bigfoot is not required to disprove the existence of Bigfoot. The non-believer in the Loch Ness Monster is not required to disprove the existence of Nessie. It is the job of the Bigfoot believer and the Loch Ness Monster believer to prove the existence of Bigfoot or the Loch Ness Monster. Theists make a positive claim. It is not up to the non-believer to disprove the claim. It is up to the theists to prove the claim. If they cannot prove their claim, then no one is unjustified for not believing the claim.
After all else fails, it does no good to fall back on the old stand by of "You cannot prove a negative". This little saying comes from folk logic and is false. If we allow that a negative cannot be proven, then we would have no way of making sense of anything. We would have to suspend judgment on everything from the existence of leprechauns, fairies, vampires, werewolves, and rival gods. The claim that you cannot prove a negative is, itself, a negative that cannot be proven, if it is true that you cannot prove a negative.
Finally, no atheists condone violence against any person, regardless of religion. Granted, there are atheists, just as well as believers, who have done despicable things (although religion takes the lead in the violence department). However, by a great majority, the weapons of the atheist are not racks and thumb screws, or any other kind of violence. The atheist's weapons are science, reasoning, logic, pen, and paper (or online forum).