The Cosmological Argument has been around for centuries. Some of the more important proponents of it are St. Thomas Aquinas and Samuel Clarke. The essential premise of this argument is that there must be a cause for everything. The world exists, and since the world exists, it had to come from somewhere.
Everything that currently exists has a cause. The causes for things that exist also had a cause before that. And those causes, likewise, had causes of their own. This string of causes could go on and on and on, but eventually, there has to be an original cause. For example: An apple tree was “caused” by a seed. This seed came out of an apple. This apple came from totally different apple tree. This process can be said to have been happening for thousands or even millions of years, but the first seed had to come from somewhere. We can say this about all forms of life and all objects in the universe. Everything that is finite (has a beginning and end) must have some sort of cause.
Since it is unreasonable to say that finite things have always existed, we must determine an original cause. The Cosmological Argument calls for an original cause that is eternal and has always existed and never had, nor needed, a cause of its own. Since it is necessary to have some sort of original cause, it is very likely that some sort of infinite God is the cause of all finite things.
A popular Atheist response to the Cosmological Argument is the Big Bang. This theory states that with a giant flash, the entire universe exploded into being. I think it is important to note that this theory is the best attempt to explain the world without God. The people who created it and hold to it begin by not believing in God, and are trying to find a way to explain the Universe’s origins. While I suppose one could hold to this argument, I just do not see the rational in thinking that gigantic stars, planets, and other things that exist exploded out of nothingness. Another problem with this argument is that if the Universe did begin with an explosion, the Universe should be spreading out at a slower and slower rate. But, the Universe is actually expanding at an accelerated rate, and this makes an explosion at the beginning much less likely.
Either you can believe that all things mysteriously appeared out of a giant explosion (although, one must wonder where the explosion itself came from) or you can believe that there is an infinite God, who has always existed, and who created the world. It seems rational to me, then, to believe in God.