NOTE: This article is adapted from a previous writeup on the topic I wrote many years ago.
For some of us, the question of "Is there any evidence, or proof, that God exists?" is a strange one, akin to asking "Is there any proof that you have a father?" But many fellow believers are often stumped by this question, so in this article I will endeavor to lay out some simple logical arguments that serve as proof, not just of the existence of God, but that there must be a personal, intelligent, infinite, and eternal Creator God.
Time is regressively finite, this means that you cannot go infinitely into the past, because to reach "now" there must have been a finite number of events leading up to it, or else we would never reach this moment. This is an important point to understand, so let me use a simple illustration: if I promised to give you a precious pearl after an infinite amount of time, when would you receive the pearl? The answer is "never", because you would never reach the end of that infinite amount of time in order to receive your pearl. If this very moment is your precious pearl, and I had made my promise an infinite amount of time ago in the past, you can see that it is impossible for us to have reached this moment. For us to reach this moment, by necessity there must have only been a finite number of time leading up to it.
Therefore, there must have been a first event, from which we measure all other events and the rest of time, and in the material world, that event requires matter. Given the logical impossibility of self creation (a law of logic called "ex nihilo nihil fit", which comes from the Latin phrase that means "from nothing comes more nothing"), there must be an agent outside of the limits of space and time (i.e., that is infinite and eternal), with the ability to create, that is responsible for that first event. This agent or entity is what we define as "God". Therefore, not only does God exist, but God must exist, due to the existence of everything around us. This is the trivial part of the proof. The question is more a matter of who, or what, this agent is.
There are many positions on defining the nature of this Creator God, and it is important to address each one.
Pantheism, which states that "god is everything", is rejected as false because "everything" cannot be God, since that would force God to be bound by the limits of creation, i.e., space and time, and, by definition, God cannot be (this would violate the law of non-self creation). Therefore, while creation comes from God, and God can interact with creation, creation itself cannot "be" God.
Deism states that God created everthing, "wound up" it up like a clock, and then "released" it to go off on its own, without any further divine intervention. Deism is rejected for several reasons, such as Chaos Theory and Newton's Second Law of Thermodynamics (Entropy), which observe that things (material systems) tend to become more disorganized, since they are at their most stable when disorganized. In other words, for things to become more "organized" they require external intervention.
A good illustration of this is to note the component parts of a complex system, like a LEGO design, and ask if it is easier to arrange them into a recognizable design or to scramble them. Or, given a set of LEGO pieces, which is easier to do by mistake: to organize them or to disorganize them?
Deism serves as the safest bail-out for those who wish to reject the existence of the god of any of the monotheistic religions, without rejecting monotheism itself.
As a side-note, even evolution requires a capable, guiding, controlling, intelligent entity (or entities) to cause the generation of new information -- such as DNA, for example. Simply put, and without going too deeply into the topic of evolution (for the curious, I'm a 6-day creationist), creation needs God to prevent it from destroying itself... from becoming more "disorganized". From a theological standpoint, this can easily be observed by how the evil inclinations of man have tangibly been restrained by something outside of mankind itself. Humanity has the nuclear capability to blow up our planet 100 times over, and despite never-ending armed conflicts, it still has not happened.
Polytheism is rejected due to the definition of God given above, which lays out the requirement that God be infinite. There cannot be multiple distinct entities all having distinct infiniteness to themselves. However, multiple entities having distinct eternality (infinite in time) would not violate the principle. This infiniteness, usually contained within the definition of the term "divine nature", can however be shared without conflict, and is what allows for doctrines of the nature of God that include a shared unity of distinct individuals (i.e., distinct "personhoods"). This is just a complex way of stating that the doctrine of the Trinity (which is almost universally considered the most difficult Christian doctrine to explain) does not contradict the one-ness of God. The doctrine states that there is only a single deity (there is only one God) but that deity is present and coexisting in 3 eternal persons, all sharing the same divine nature.
To further see why polytheism must be rejected, we return to the definition of God as the entity responsible for the origin of Creation and the existence of matter. If we were to have multiple gods, then the key question to ask is: which of those "gods" is the infinite one? Which is the Creator?
Polytheistic systems hold limitations on the finiteness and temporality of their gods, and if any of these gods can cease to exist, they are not eternal nor infinite, and hence fall outside of the definition of "God".
It is important to mention Henotheism, a sub-class of polytheism that states that while there are multiple gods, only a subset of these (one or more) are "worthy of worship". The religious belief systems of the Jehovas Witnesses and Mormons (also known as the "Church of Jesus Christ of Latter Day Saints") are henotheistic, and therefore polytheistic. As such, they must also be rejected as false.
There can only be one God.
It can be argued that God is personal (as in "having personality") by the fact that the work of creation required design and therefore creativity and intelligence, which themselves require some form of personality, given the decisions involved in the process. Creation can't be argued to have been the result of random processes, because it would not have led to the highly organized nature of all that exists (as stated in the section on Deism above), this especially in light of biological systems which are irreducibly complex -- systems that need all parts exactly as they are in order to function as they do.
So we have an infinite, eternal, personal God with the ability to create, who is separate from His creation, in some form of monotheism. The main religious groups holding that description of their god are the so-called "Abrahamic faiths": Judaism, Christianity, and Islam. There are also subgroups of other large religious groups (such as Buddhism and Hinduism) which have variations in their teachings that affirm monotheism where their other branches do not.
We therefore now face the matter of unveiling the identity of this Creator God. If indeed God is personal, it would be natural to see or expect some form of interaction with His creation, other than merely maintaining it. That is where revelation kicks in. Of course, that's a concept that becomes much trickier to deal with, and is where the more logical, and drier, part of the proof ends, and the matter of faith begins. If God has chosen to reveal Himself, then how does (or has) He?
People who claim to receive messages from their god are referred to as "prophets" by those who recognize them as such. The Bible says that the sign of a prophet is complete inerrancy when speaking on behalf of God, and I find this to be a good, logical, and highly useful standard to hold anyone claiming to be a prophet to. Using this standard, we can go through the process of elimination to find true prophets by removing those who don't exhibit that required inerrancy.
Any group having a leader or prophet that uttered false prophecies, or that has taught "revealed truths" that contradict prior revealed truths from their god can be immediately and trivially disqualified as false.
Arriving some 500 years after Christianity, Islam positions itself in the Quran as the diametrical opposite of Christianity by explicitly stating that "Allah did not beget a son nor was he begotten". This means we can eliminate one by proving the other. As a Christian I am more informed on Christianity, so that is the thread I will pursue below.
In just the historical person of Jesus alone, there are more than 360 Old Testament prophecies that were fulfilled, of which 190 could only have been fulfilled in Him and no other person in history. There are ample records from historians that did not believe the theological claims of Christ but who did confirm other historical claims about Him as an individual, such as the fact that He was indeed a real person who lived, the region in which He lived, and some of the events chronicled in the New Testament.
Fulfilled Old Testament Messianic prophecies included the familial lineage of Christ, historical timeframe of His appearance, and several of the miracles and signs He performed. In fact, since the Messiah was prophesied to appear in the time of the Second Temple (Haggai 2:6-9), and the Second Temple was destroyed in the year 70 AD, if the Messiah did not appear before that, then the prophets of the Old Testament are proven false, and Judaism must be rejected.
In fulfilling the prophecies of the Old Testament, Jesus proves the prophets of the Old Testament true.
The most sizable branch of modern Judaism is called Rabbinical Judaism. Modern Judaism is of course very different from the Judaism of the Old Testament, not just culturally, but more importantly in terms of beliefs and practice. With the destruction of the Temple, ritual sacrifice required for atonement on Yom Kippur was now impossible, and there was a transition to hold the Talmud and writings of Rabbis as authoritative, nearly on par with the Tanach (the Hebrew word for what Christians call the Old Testament). There are two other branches of Judaism, the much smaller branch called Karaite Judaism, which rejects the authority of the Talmud, and of course Messianic Judaism, which is made up of the Jewish Christians who keep their Jewish identity and traditions.
One of the distinctive beliefs the non-Messianic branches of Judaism hold about the Messiah is that he has not yet come, and as we saw above, this puts them at odds with their own prophets who lay out the timeframe for the appearance of the Messiah. With this window of time come and gone, we must reject these branches of Judaism as false, whether we believe Jesus is the Messiah or not.
The historicity of the person of Jesus gives us 190 reasons to believe, and along with finding no contradictions in the text this shows that the God revealed in the Old Testament is the true Creator God, and that we can accept the New Testament as reliable truth, to the exclusion of all other belief systems. All other systems are rejected.
Once we know and have settled upon the truth of God's existence and His identity, how should we respond? How does that now change how we live, or understand the world? Fortunately, God has also revealed to us how He wants us to respond to this knowledge, and to Him.
The Bible says that our sin, those bad things we do that offend God, spiritually separates us from Him, and while in that state of separation, God does not hear us, and we cannot have fellowship with Him.
It is only when those sins are paid in full that we can experience fellowship with God, and that's what Jesus did on the cross, paying for the sins of His people in full, making it available for us to be reconciled with God. And the Bible says that He will not turn away anyone who seeks Him.
We must acknowledge that we are sinners, that we have sinned against a Holy God. We must repent (which means "to turn away") fully of our sins, and understand that there is nothing we can do to earn salvation, and that no good deeds or personal righteousness will ever be enough for us to deserve God's forgiveness. Salvation coupled with forgiveness is the exclusive gift of God, available only through the finished work of Jesus, the Son of God, and nobody else. It is then that our sins are forgiven in full, and we enter into that close relationship with our Creator God.
There is salvation in no other, because if God is infinite, any sin against Him is an infinite offense, and therefore requires an infinite payment. Only God can make an infinite payment, and if Jesus is not God, then His payment is not enough, and we have no hope for salvation..
Now that you know, you are left without excuse. Do not let this opportunity pass you by, call upon the God who Created the Universe, who personally knit you together in your mother's womb. Forsake your sin and place your trust only and fully in His Son Jesus Christ. Today is the day of salvation, do not wait for the end of an infinite number of events to cast yourself into His loving arms and receive the pearl of His forgiveness and salvation.
Read more here: "What is the Gospel?"