You'd likely agree with me that the co-discoverer of Calculus was a smart guy.
Gottfried Wilhelm Leibniz (1646-1716) was a German mathematician, logician, and philosopher. Leibniz is well known for his mathematical discoveries, but he's also recognized as the person who popularized what many say is the single most important question ever asked: Why do we have something rather than nothing at all?
In his short work, Principles of Nature and Grace Based on Reason
, Leibniz presents and answers the question in the following way:
Now I must move up to the metaphysical level, by making use of a great though not very widely used principle, which says that nothing comes about without a sufficient reason; i.e. that for any true proposition P, it is possible for someone who understands things well enough to give a sufficient reason why it the case that P rather than not-P. Given that principle, the first question we can fairly ask is: Why is there something rather than nothing? After all, nothing is simpler and easier than something. Also, given that things have to exist, we must be able to give a reason why they have to exist as they are and not otherwise. Now, this sufficient reason for the existence can't be found in the series of contingent things…it must be something that exists necessarily, carrying the reason for its existence within itself; only that can give us a sufficient reason at which we can stop. And that ultimate reason for things is what we call 'God'." 
Leibniz believed that God was the best explanation for why everything exists. From his writings, many philosophers and theologians have created their own way of stating his conclusion. For example, William Lane Craig presents his case in the following way:
1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause.
2. If the universe has an explanation of its existence, that explanation is God.
3. The universe exists.
4. The universe has an explanation of its own existence [and that explanation is not found in the necessity of its own nature].
5. Therefore, the explanation of the universe's existence is God.
My way of stating the position is a little more personal / informal, and is something I call my '30 second argument for God':
1. I exist.
2. If I exist, something must have always existed because you don't get something from nothing.
3. There are only two choices for an eternal 'something': (a) The universe; (b) God.
4. The universe is not eternal.
5. Therefore, God exists.
Let me quickly walk you through the individual points and demonstrate why I think this argument is reasonable and sound.
Yes, You Exist
A student in a philosophy class once asked his professor, "How can I know that I really exist?" The professor looked down the glasses that were on his nose at the student and responded, "And who may I say is asking?"
It's simply self-defeating to contend you don't exist because you have to exist to ask the question. As the mathematician Descartes (also a believer in God) famously said, "I think, therefore I am."
Nothing is Really Nothing
No matter how hard atheistic scientists such as Lawrence Krauss try to argue in books like A Universe From Nothing
that you can get something from nothing, you really can't. Krauss redefines 'nothing' to be physical systems such as the quantum vacuum, so his widely panned book both fails to answer Leibniz's question and embarrasses the physicist in the process.
'Nothing', as Aristotle said, "is what rocks dream about". As an example, if you ask me what I had for breakfast today and I say 'nothing', you likely won't ask me how my 'nothing' tasted.
The reason everything is here — including you and me — is because something has always been here. In the end, the believer in God and the atheist are really just arguing over what that 'something' is.
Only Two Choices
Some atheists have surprised me by saying we have more than two options available where an eternal 'something' is concerned. However, the vast majority of thinking atheists acknowledge that if the universe isn't eternal, then God is the only other possibility.
Make no mistake about it — God is not 'snuck in' as one of the choices via some theological bias, but rather a creator is something absolutely essential if the universe has an explanation for its existence (i.e. it is not eternal). The universe comprises all of space-time reality and if it has a cause, it, as Craig says, "proves the existence of a necessary, uncaused, timeless, spaceless, immaterial, personal Creator of the universe. This is not some ill-conceived entity like the Flying Spaghetti Monster but an ultramundane* being with many of the traditional properties of God." 
It truly is a question of either matter before mind or mind before matter.
Ruling the Universe Out
If, as skeptics say, they go where the evidence leads, then they should be led to the conclusion that the universe is not eternal.
Empirical evidence such as the second law of thermodynamics, the fact that the universe is expanding, the echo from the big bang discovered in 1965, the temperature ripples found by the COBE project in 1992, Einstein's theory of relativity, and more all point to a non-eternal universe.
Attempts at positing a supposed multi-verse (an ensemble of universes) have failed to deliver any real evidence that such a thing exists. Moreover, research done by eminent scientists point in the opposite direction. Dr. Alexander Vilenkin concluded his "State of the Universe" paper, which was presented at the 70th birthday celebration of Stephen Hawking that took place in January 2012, by saying "all the evidence we have says that the universe had a beginning." 
Further, Vilenkin's proof developed with Arvind Borde and Alan Guth, shows that any universe which has, on average, been expanding throughout its history cannot be infinite in the past but must have a past space-time boundary. This includes any supposed multi-verse. Since our universe and any multi-verse have a beginning, they have a cause and are not eternal.
The Fish You Can't Drown
As Leibniz concluded, God is the best explanation for why everything exists. All the effort that Krauss and other atheists put into trying to deny God is, in the end, an exercise in what philosophy calls "drowning the fish". You can pile all the ocean's waters on the animal (in this case, God) in an attempt to drown it, but in the end, the fish is still there affirming its presence.
Note that this argument for God doesn't go so far as to try and prove the God of the Bible, but rather seeks to establish the reasonableness of an eternal mind that exists beyond this physical universe. However, the fact that logically ascertaining the attributes of this creator from its effects produces a list that matches up quite well with the God described in Scripture certainly lends support for the idea of the Christian God.
Nearly 300 years after Leibniz reached his conclusion that God is the best explanation for why everything exists, today's scientific discoveries and rational thinking are proving him right. But then, good science, good philosophy, and good religion should always eventually arrive at the same conclusions.
Extending or being beyond the world or the limits of the universe.
1. G. W. Leibniz, Principles of Nature and Grace Based on Reason
, 1714. http://www.earlymoderntexts.com/pdf/leibprin.pdf
2. William Lane Craig, On Guard
(Colorado Springs: David Cook, 2010), pp. 53-65.
3. Craig, pg. 60.