The Christian Perspective
In the words of the late Greg Bahnsen, the most basic proof of Christianity is that if it were not true, it would be impossible to prove anything at all.
If the non-Christian worldview is true, the laws of logic are not valid. Therefore, even though non-Christians use logic to interpret evidence, they have no real justification for doing so. In the non-Christian worldview, logic is not something that can be trusted.
Christians alone do have a basis for recognizing that the law of non-contradiction applies everywhere and at every time, past, present and future. Our basis is the character of our God.
According to the Bible, the Creator of all things is consistently logical. He cannot lie (Hebrews 6:18, Titus 1:2) and He cannot deny Himself (2 Timothy 2:13).
Further, all truth and knowledge is in Christ (Colossians 2:3), who is God (John 1:1), and who created all things (John 1:3).
As Christians we know that all things have been created by One who is consistently logical, and therefore the laws of logic are both universal and invariant. Because He holds the keys to all knowledge, we also know that logical knowledge is possible.
Christianity, as we see, has grounds for trusting logic -- for claiming that the laws of logic are always true, a claim that other worldviews have no basis for making.
An easy way to demonstrate this latter point, that non-Christian worldviews deny the validity of the laws of logic, is to begin at the beginning.
We see that time past has ended. To avoid infinite regress, we must acknowledge that it also began.
Infinite regress is logically incoherent. To suggest that there have been an infinite regress of past moments is to suggest that we have come to the end of an infinite series. An infinite series, however, is by definition a series with no end. So this would mean that we have come to the end of a series with no end, which is logically incoherent.
Infinite regress would mean that we have iterated, one-by-one, through every single item of an infinite series. But an infinite series always has more items than those that have been iterated through. We would have iterated through something that cannot be iterated through, which is logically incoherent.
If we were to go backwards through each previous moment in past time, and there were an infinite number of past moments, there would necessarily be some moment in the set of previous moments that we would never, ever get to. If that were not the case, it would not be infinite. If there is some supposed prior moment in the set of previous moments that we could never get to while iterating backwards through all previous moments, then, iterating forward from that moment to the present moment, we would never arrive at the present moment for the same reason that going backwards we could never arrive at the previous moment -- namely, the infinite (or unending) number of moments in between the two.
Infinite regress would mean that we have completed something that cannot be completed. We have traversed something that cannot be traversed. We have itemized what cannot be itemized, counted what cannot be counted, spanned what cannot be spanned.
Infinite regress violates the logical law of non-contradiction.
So we quickly see that Time Past is not infinite, and must therefore have been finite.
THE BEGINNING WAS CAUSED
To suggest that time began uncaused, or anything beginning uncaused for that matter, is absurd... it is the same as suggesting that having nothing and adding nothing to it, something results, or in other words:
0 + 0 > 0
I like to refer to this kind of thinking as "Atheist Math". In Atheist Math, zero is not equal to zero, violating the logical law of Identity.
Ultimately, there is some kind of cause of time, and to again avoid infinite regress, there must be an ultimate First Cause of time.
THE CAUSE IS ETERNAL
If the cause of time were somehow temporal, it would require the passing of time to exist, making what's known as a circular dependency, another type of infinite regress, which violates the logical law of non-contradiction.
Therefore, being not bound by time, it is, by definition, eternal (Deuteronomy 33:27).
Since it is outside of time, it does not inherently change over time, which means its inherent qualities are unchanging (Malachi 3:6).
THE CAUSE IS PERSONAL AND RATIONAL
Since it is the First Cause, it must be uncaused.
Since it is the uncaused first cause, it is self-directed and self-motivated and acted volitionally, which, simply by definition, makes it personal (Job 13:8). If it were not personal, it would not be capable of self-directed, self-motivated, volitional action, preventing it from being the First Cause. It would be the First Cause and not be the First Cause, violating the logical law of non-contradiction.
Further, if the cause of our beliefs and conclusions were not rational, there would be no reason for claiming that our own beliefs or conclusions are rationally determined. Every thought we have would be irrational without a rational God!
ATHEISM THUS INCOHERENT
Thus, a personal, unchanging and eternal uncaused First Cause clearly exists because of the logical impossibility of the contrary. This rules out all possibility of Atheism, Agnosticism, Ignosticism, and any worldview that claims that past time has been infinite, or that the Divine Initiator is temporal.
Every temporal action or activity has to have a personal, uncaused First Cause ultimately behind it, from the movement of light away from the sun, to the decision to share your last chocolatey caramel Rollo with the person you love, to our very recognition of right and wrong. Any event that takes time had to begin, since time itself began, and if that event began, then it must have been caused, and if it was caused, then there must ultimately be a personal uncaused First Cause behind it.
What's more, if there are multiple personal uncaused First Causes, multiple ultimate authorities, there would be no single source of authority. This means that no one could actually justifiably guarantee how things will operate in the created realm. One god may contradict another god, and then things that truly are... may not be! There would be no way for either god to guarantee that this will never happen, making non-contradiction an unreasonable test of truth. This would again render knowledge of any kind absolutely impossible.
Further, regarding this one God that must exist, since He alone is the source of all things in order for rational thought to be possible, it follows that He alone is also the reason for all things. For us to think rationally, our programmer must also be rational (and eternally so), meaning that He Himself must eternally conceive of Himself as His own ultimate reason for everything that occurs. This conception of Himself will eternally be the exact representation of Himself, sharing divine sovereignty, since this conception is the reason for everything that occurs. This demands that deity be shared between the conceiver and that which is conceived, between God and God's image. Unitarianism denies that deity is shared in any sense, making any imagined unitarian god irrational.
WE DON'T DO WHAT WE OUGHT
We are each keenly aware that this unified personal ultimate authority, or "God", has caused us to have a guiding sense of moral justice which we call our conscience, and we are also aware that we are unable to perfectly obey it.
Man's disobedience to the ultimate authority serves as a foundational problem resulting in the establishment of essentially every religion.
However, non-Christian religions tell us that the solution is that we must do better -- that we must be perfect -- that we must fix the problem of sin.
WE ARE IN DEBT
God has provided us with time in this life during which we ought to obey the moral code He gave us. If any amount of time is spent in disobedience, we have spent that time in a way other than we should have. Since the time was provided to us by the God that also informed us of how we should use it, and since we have not used it all as we ought, to right this wrong, additional time must now be spent the way the wasted time ought to have been spent.
Among other things, we owe God time.
WE CAN'T FIX THE PROBLEM
We cannot create additional time for ourselves. Any time we have was provided to us by God to be used in obedience to Him. Any more time that God gives us will only increase our debt to Him, and, since the ultimate authority is absolutely united, there is no other way for us to get extra time.
Suggesting that we can pay back our debt of time in submission to our Creator "on our own" is really no different than suggesting that we should borrow from our lender to pay him back for money we borrowed from him earlier. The debt would never get paid that way.
ALL REMAINING WORLDVIEWS INCOHERENT
To claim that we can pay off a debt to our Creator is to claim that we own something that He has no authority over. But we have already established, via the necessary perfect unity of all Personal First Causes, that absolutely everything we own comes from Him, and that He has authority over all of it.
Thus, to suggest we can pay Him back for what we have misused is to suggest that the One in authority over everything is not in authority over everything. This again violates the logical law of non-contradiction, disqualifying all remaining worldviews.
Christianity, by contrast, tells us the only possible truth -- that we aren't in charge, and we can't be perfect: we can't fix the problem of sin.
GOD CAN FIX THE PROBLEM
However, self-evidently, the unified One in ultimate authority can fix the problem. (Mark 10:26-27)
In fact, He has.
Only Christianity tells us about the God who loves us so much that He took our penalty on His shoulders -- it tells us that, in addition to the Son's eternal and perfect obedience to the Father in our place, He also shed His own blood on the cross to pay the debt of our sin, provided we accept His free gift (Romans 6:23; John 3:16; Acts 20:28; Revelation 1:5; Romans 10:9).
Only Christianity fully recognizes the reality of sin, the inability of man to fix the problem, and the graciousness of a perfect God to solve it for us.
Ultimately, all the clear and unquestionable proofs in the world cannot and will not convince a rebellious person to trust his Creator, because he intentionally suppresses the truth in unrighteousness (Romans 1:18).
Some claim that God's existence cannot be proven, since, if we could prove His existence, we would not need to have faith. However, this is simply not the case. God tells us that everyone knows He exists (Romans 1:20). Trusting the God that we all know exists is what the Bible calls "faith". Without this faith, it is impossible to please God (Hebrews 11:6).
So we see that the Christian has every justification to assert his worldview as absolute truth, while the non-Christian, were his views true, would be incapable of asserting anything at all. If Christianity were not true, the laws of logic would be invalid, and every assertion would be meaningless.
The most basic proof of Christianity is that if it were not true, it would be impossible to prove anything at all.
How Can We Know the Bible is Valid?