The cosmological argument, or "first cause" argument, takes the existence of the universe to entail the existence of a being that created it. It does so based on the fact that the universe had a beginning. There must, the first cause argument says, be something that caused that beginning, a first cause of the universe. The cause is assumed to be God.
The argument runs like this:
- Everything that exists must have a cause.
- If you follow the chain of events backwards through time, it cannot go back infinitely, so eventually you arrive at the first cause.
- This cause must, itself, be uncaused.
- But nothing can exist without a cause, except for God.
- Therefore, God exists.
The most concise answer to this argument is: "Who created God?", which begs the question "who created the creator", and on and on ad infinitum. This is also related to the phrase "It's turtles all the way down".
There is a contradiction between the first statement and the second statement. If "everything that exists has a cause" then there cannot exist anything that does not have a cause, which means that there is no first cause. Either some things can exist without causes, or nothing can. It can't be both ways.
It is not necessarily the case that there are not an infinite chain of causes and effects. We know that our universe had a beginning (the big bang) but we don't know what occurred in the first split second after the big bang, nor can we comment on anything that came before it. There may have been another universe that gave birth to this one. The universe may even exist inside a meta-universe, which does not have a beginning.
On the other hand, even if we grant that a first cause exists, it makes no sense to assume that it is any kind of god, let alone Yahweh. The idea of an intelligent, universe-creating god "just existing" is far more difficult to explain than the universe itself "just existing". Intelligence is one of the most complex things we are aware of in the universe. To assume a being who is so intelligent that it can design an entire universe, as well as micromanage the personal lives of billions of people on earth through prayer, would require an enormous amount of explanation.
Christians try to avoid this issue by saying "God does not need a cause because He is outside of time." This is a glib non-answer. If all that is required to get around the first cause argument is an entity that exists outside of time, then all we need to do is postulate a single particle that exists outside of time and triggered the big bang. It need not have any special powers at all. Besides, this particle might even exist, depending on how you define "outside of time". Photons, light particles, do not experience time, since they move at the speed of light. Therefore, according to this argument, light can pop into existence wthout cause.
Theists will object that this particle should have a cause. But they have already refuted this argument by granting that there exists an uncaused cause in the first place. If God can exist without a cause, why not a particle? Why not the universe?
This argument can be associated with the First Law of Thermodynamics, which says that the amount of mass and energy in the universe will remain constant. They cannot prove the proposition "Everything has a cause." without proving the First Law of Thermodynamics. Since this law only talks about mass and energy, space-time itself can, as far as we know, pop into existance whenever it wants. Some scientists, expecially those who favor M-theory, say that, in a multi-universe model, when two universes colide it could create a matter and energy in a big bang, which would be the cause of mass and energy. Therefore, it is entirely possible for the universe to arise from material sources.
See also kalam.