First, let’s get one thing out of the way: there is existence as a concept, an idea in the mind. As far as that goes, every god that man has created exists, as a concept in the mind of man. Then there is existence, as in, guns exist and they can do a lot of real harm; that needs no proof, as we have had proof of that for centuries.
Having said that, I would then say that no, Yahweh, the god of the Bible, doesn't exist. That was the short answer, the long answer is why I'm writing this essay. I will demonstrate why I think it is impossible for the biblegod to exist. If this deity is described in a self-contradictory manner, then it follows that it is non-existent, according to the law of contradiction; and biblegod most certainly falls into this category.