I'd say we can't possibly know. There may be, there may not be. I personally don't believe that if there is a God (or gods), it would be anything even remotely like the one described by any major world religion. It may be, but it seems highly improbable to me. If by 'God' you mean a sentient being that conciously or unconciously triggered the creation of the universe, then I'd say I don't have any evidence either way, hence it's possible. Add omnipotence to the mix, and I'd still say possible, but less probably simply because there's still no evidence, but instead of 2 clauses to the description (Sentience and Universe Creation), there's a third, Omnipotence. The Gods represented by major world religions have thousands of clauses to their descriptions, from their appearance, to nature, to the individual acts they supposedly performed. In the absence of any evidence, I hence consider them to be very improbable. (In the case of the Deities described by movements that have been entirely contradicted by our knowledge of modern science, such as young-earth creationism, I would say that they are fundamentally almost entirely impossible, although obviously, given a Deity with omnipotence, you can never rule anything out entirely. Omnipotence is annoying like that.)
The question about the existence of "God" is inherently loaded to begin with, because it's already assuming monotheism, patriarchy, and, arguably, Judeo-Christianity. Nevermind . . .
If there is one god (and not twelve of them), there is no scientific reason whatsoever to assume that any particular religions, "world", "major" or otherwise, have nailed him down. Because they all come from a particular culture with its own cultural bias. For example, if the Christian god loves us all, why are the Jews his "chosen people". That's bullshit favouritism right there. Why were all his prophets Jewish, why didn't the Bible fall from the sky written in Italian over Italy, Irish over Ireland, Japanese over Japan, German over Germany, et cetera. Why only reveal yourself to one wandering tribe in one corner of the world, and then sit back and watch it gradually spread to other cultures, with all the conflicts, misunderstandings and mistranslations that brings?
The Judeo-Christian scriptures have Yahweh declaring "we have made man in our image". Well, man is black, white, yellow, red and brown. What race were Adam and Eve? Jews? So is God a Jew? Well maybe that god is. The Book of Genesis was written by Jews for Jews.
Edit: Hah. "Nailed him down".