Many cosmological arguments, though not all, argue that the universe began to exist; and since everything that began to exist was caused by something else, the universe was caused by something else. With Big Bang cosmology this point has received empirical confirmation: according to the Big Bang, the universe -- that is, matter, energy, space, and time -- began to exist. Thus, something that exists independently of matter, energy, space, and time brought them into existence.
One objection to such arguments is that, even if the Big Bang has a cause, there's no reason to think this cause is God, much less the God of the Bible. I have to admit, I've never felt the force of this objection. I mean, is there any other issue where if you don't prove everything about it with a single argument, you prove nothing about it? The Big Bang only proves that there is an immaterial, spaceless (hence omnipresent and transcendent), timeless, and unimaginably powerful cause of the universe, and the response is, "Yeah, so?" Really? Of course the Big Bang doesn't prove that the cause of the universe is the ground of morality, of course it doesn't prove that Jesus rose from the dead, etc. But has anyone ever claimed it does? Why can't it function as part of a cumulative case argument?
What this objection is really focusing on, I think, is whether the cause of the universe is a mind -- or at least, as C. S. Lewis puts it, "more like a mind than it is like anything else we know". A cause that was not a mind would be mechanistic, since a mechanistic cause is one which produces its effect automatically. That is, if the cause is present, the necessary and sufficient conditions for the effect to take place are met; and since the necessary and sufficient conditions for the effect to take place are met, the effect takes place.
But since the scientific evidence proves that we are dealing with the beginning of time itself, the cause of the universe must be timeless. So is it possible to have a timeless mechanistic cause that produces a temporal effect (in this case, the universe)? It is difficult to see how this would be possible. A timeless mechanistic cause would produce its effect timelessly, since the necessary and sufficient conditions for its effect's occurrence are timelessly present. But in the case under discussion, the effect (the universe) is not timelessly present, and yet must have a timeless cause, since time is part of the effect. Therefore, the cause of the universe cannot be mechanistic or automatic; it must be non-mechanistic. It must be an entity with the capacity of choosing to create the universe as a finite, temporal effect. And the ability to choose is an inherently mental act. Therefore, the entity responsible for creating the universe must be a mind, a personal agent with free will. As William Lane Craig puts it in The Kalām Cosmological Argument, "For while a mechanically operating set of necessary and sufficient conditions would either produce the effect from eternity or not at all, a personal being may freely choose to create at any time wholly apart from any distinguishing conditions of one moment from another. For it is the very function of will to distinguish like from like."
So it seems that cosmological arguments based on Big Bang cosmology prove, among other things, that the cause of the universe is an incredibly powerful Mind. This obviously matches up with the Judeo-Christian concept of God. One could still object that the Judeo-Christian God has other traits that these cosmological arguments don't prove, but I'm afraid I'm too overawed by what they do prove to think this objection amounts to much.
(cross-posted at Quodlibeta)