"The only system of thought that Christ will fit into is the one where He is the starting point." --Athanasius
We begin with God and explain the universe of ideas, we don't reason to God but from God!
Unbelievers don't want to believe in evidence because the evidence is stacked against them and they're looking for a loophole to justify themselves. Find out for yourself: Ask them just what evidence they have found that proves there is no God! They will have to answer far more questions about God's existence than they can argue against God, as we will see. God needs no evidence to exist and merely assumes you have realized His existence--He doesn't need to prove Himself! The Bible even presupposes and assumes God: "In the beginning God...." The Bible doesn't seek to apologize for God or offer any proof but even says those who deny Him are fools. It is a matter of the heart, not the intellect, for denial of God is intellectual suicide and people suppress the knowledge they do have. They are in a state of denial! It is convenient for their lifestyles to deny a God who is the moral center of the universe.
What we know about God is not a matter of speculation or conjecture, but revelation and faith, we cannot have laboratory conditions, put Him in a test tube, or conduct an empirical investigation on a God who is not tangible, visible, or audible to us but dwells in another dimension. He isn't subject to scientific analysis--there can be no laboratory conditions--because He's not observable, measurable, verifiable, repeatable, experimental, predictable, testable, variable, or controllable. God has revealed Himself to us and in the Bible we see this consummated, personified, and incarnated in the personhood of the God-man, Jesus Christ. Where we start determines where we will end up! We must begin with Truth with a capital T to find God. We don't start with the universe to explain God or explain Him away, but start with God and explain reality and the universe. We don't conclude with God in the equation; rather, we start with God in the equation.
Man's problem today is to forget God and take Him out of our reckoning and life's equation. God makes no apologies and owes no one an explanation for His works or actions. He is too kind to be cruel, too deep to explain Himself, and too wise to make a mistake, it has been said. The problem with the infidel is that you cannot argue him into the kingdom. There is always enough evidence or conviction for the willing but never enough for the unwilling. Even if convinced he will be of the same opinion. There isn't enough evidence to dissuade the willing, nor enough to persuade the unwilling. This is because God cannot be rationalized but only known through faith by a work of grace.
Unbelievers are people of faith too, they just place it in their own logic and philosophy and ultimately science has all the answers or can find absolute truth. Using science to harness truth out of its proper domain is not science but scientism--there are ways to truth outside of science and some knowledge isn't subject to science: ethics, morality, philosophy, theology, et cetera. The infidel puts God on trial and to the test, thinking they can judge God when He is their Judge. The point is that all knowledge is contingent except God's and we all begin our quest for it as a leap of faith, accepting something or someone's word as truth we cannot prove. The Bible says that the fear of the Lord is the beginning of knowledge! It's never a matter of reason versus faith but which set of presuppositions one is willing to accept.
We are all at the stage in our faith at the onset of believing but still need God to help our unbelief. Miracles, for instance, never force belief but only bolster and support faith and even produce a desire for more miracles. God is not in the business of miracles on-demand or doing biggie, showy, miracles to amaze us into faith. Miracles don't make faith--faith makes miracles! Everyone should realize that juries convict on the preponderance of the evidence, not all of it--which isn't available--and in the direction of the evidence. Often they must rely on merely circumstantial evidence or witnesses with little corroboration. But the biblical rule of thumb is to rule in favor of the defendant lest an innocent man perishes by mistake.
Also, history is not subject to scientific inquiry because it's nonrepeatable by nature and cannot be observed or measured. There are no living witnesses to antiquity! But the resurrection is arguably the best-attested fact in ancient times. Christ's resurrection is a matter of history and the circumstantial evidence is most compelling! In fact, Luke says there are many "infallible proofs." The Bible needs no defense or evidence for it is self-attesting and appeals to no higher authority than itself or it wouldn't be the final authority! You cannot logically say that it's true because it's never been disproved, but a person only need read it with an open mind and find out for himself--he can prove it himself! Legally, the burden of proof is always on the party disputing the validity or genuineness of the document.
The only way you can prove God is to limit Him or put Him in a box, and this cannot be done and if we could He wouldn't be worthy of our worship because the finite cannot grasp or contain the infinite. We do have arguments and evidence though for Him--and evidence isn't conclusive but only a reason to believe- but no smoking gun proof that makes us believe against our wills. He leaves faith up to our own decision but the Hound of Heaven is wooing us and is able to convict us and even make the unwilling willing and turn hearts of stone into hearts of flesh--for the heart of the matter is that it's a matter of the heart! But you cannot disprove God either, for it's illogical and impossible to prove a universal negative without being all-knowing and everywhere at once.
You can argue for God by realizing He makes sense of everything. We don't need a holy grail or theory of everything in science; what we need is enlightenment from God and return to our roots to Christianity as the mother of modern science. It's like saying we believe in the sun, not because we see it, but because we can see, and see everything else! Could you imagine someone not believing in words yet speaking them? We only believe in love because we've experienced it, not because its existence has been proven to us! Where did all the abstracts come from? For instance, what about heroism, honesty, fair play, aesthetic appreciation, conscience, good faith, altruism, fairness, equity, generosity, truth, honor, bravery, courage, et cetera? God makes sense of history and of the world, seeing it as having meaning and going somewhere, even telling a story with lessons to learn.
Even science is explained by God and wouldn't have arisen without Him in the picture. How can we explain the Big Bang or the beginning without a Beginner? If we have "creation," we need a Creator! How can we posit design without a Designer? Since we have art, that necessitates an Artist. Things appear to be in order and according to specs: what about an Orderer? They want to shun hell but they believe in justice without the Judge!
How can we explain the principle of biogenesis (which denies spontaneous generation) or that life only comes from life without a source of life? How can we see the Anthropic Principle (or the fine-tuned earth) without realizing a God of design, beauty, intelligence, harmony, and intention? It looks like our Creator intended it this way. One scientist wrote a book entitled The Privileged Planet to prove this principle. Where did the first DNA, the metabolic motor of life, come from, if DNA only comes from DNA? How can we explain the First and Second Laws of Thermodynamics without God in the calculus? If we must offer proof, so must the infidel!
Thinking in the abstract, where did love come from and how can you measure it or define it. Measuring three feet of love is absurd! How did we come to know of good and evil if they don't exist and there isn't a source? Why do we have such a concern for right and wrong and a moral compass if there isn't a God who is the moral center of the universe? How can there be purpose, design, beauty, art, order, and musical harmony without God or one of purpose, design, and intent? How can there be wrongdoing and crime without a Judge? How can there even be good without a source of good or Supreme Good as the standard? History makes no sense without seeing it as His story and having a beginning and ending or consummation and of meaning instead of being circular or cyclical? Basically, how can we believe in the existence of truth without a God of truth as its source?
Cosmologically speaking: When we realize the law of causality or of cause and effect, we realize that there must be a First Cause because an infinite regress is illogical and it's impossible to cross infinity--the chain in the link has to begin somewhere. Note that we can know nothing for sure without the principle of cause and effect! But nothing can cause itself and be its own cause, and therefore everything must have a cause except this one uncaused cause that got it all started--no beginning means being eternal and nothing would exist without this beginning; however, God had to begin everything somewhere in time, for everything captive to the time-space continuum had a beginning and God created time, space, and matter, and so had no beginning--being eternal implies having no cause. In short, God is not an effect and is independent of time and therefore needs no cause, being self-existence or dependent on no one and nothing. Indeed, there are so many constants and fixed laws in the universe that it makes it look like God has a pure mathematical mind, which is what Einstein postulated.
Note: We are the evidence: Our very existence is rigged and we are a miracle! The biggest miracle is seen in the conversion and transformation of a believer upon salvation. We cannot explain our existence, much less God's! We will find that a little philosophy may incline one toward atheism, but true knowledge begins with God in the equation we may think we can reason to God, but reason tells us some things are beyond reason; we can only reason because of God of reason and our gift of reason!
Christians have simple, not simplistic faith, but not enough to be an atheist! The Bible says that unbelievers suppress the truth; this implies they know the truth! We must ask the unbeliever if he would repent and receive Christ as Lord and Savior if given sufficient evidence. The problem is always the same: Not that they cannot believe but they won't and will not believe! Believers are not Christians because of the evidence who were convinced against their will, but because the Holy Spirit made believers out of their sincere hearts, wooing them and turning hearts of stone into ones of flesh.
The conclusion of the matter is making decisions based on facts and evidence, not whim or feeling--without which it ends up being merely blind faith. We must be willing to follow the evidence with an open mind wherever it leads. We will never find truth--and all truth meets at the top according to Thomas Aquinas--unless we admit we could be wrong, as Socrates said. In other words Soli Deo Gloria!