William Lane Craig notes:
"If God does exist, He is certainly capable of communicating His truth to you in an interior way as well as through external evidences... many Christian beliefs are beliefs warranted to us by ...God's own testimony [inside]. Don't be too quick to dismiss it, lest you fail to hear the voice of God speaking to you."So having said all that, you may actually agree with Craig that inner evidences are evidence, but your question is simply asking, "are there other, publicly available evidences?" I do not disagree that if the case for God relied ONLY on inner evidences it would be a much less compelling case.
It turns out the case for God's existence is very strong because it includes so much of the type of evidence you are interested in. So on to that evidence. There is so much material here I can merely describe 4 excellent, non subjective, non faith-based arguments. I'll go more in-depth on the first, but I'll link you to 5 minute videos from Dr Craig's excellent YouTube page which will give you a primer on them all.
1. THE EVIDENCE FROM A BEGINNING
This is drawn from the core question, why is there something rather than nothing? Everyone knows that things we see now are results of past causes. You're here because of your parents, and they because of theirs and on back. But does this chain of cause and effect go back forever? Atheism requires that it does, but is this reasonable?
There are good reasons to think both scientifically and philosophically that the universe cannot be infinite in age. Philosophically, actual infinites of anything usually lead to absurdities. Imagine I went to heaven and God said, "you have to count whole numbers up to infinity before you can get in, but don't worry i'll give you as long as you need." When I'm at 14 quadrillion, God gives the same assignment to another guy. I think, man I'm so far ahead of this guy! But actually, we both still have the same infinite number of numbers to count! And therefore, we will both never get in!
Well, if you can't cross infinity positively, how can you cross infinity going backwards? To say it another way, how can you go from minus infinity events to today? It's impossible, because it's the same distance! If the series of events in the past started infinitely long ago, it would have never gotten to today, because you would never have reached the first event to start the chain!
So the argument for God in all this is as follows: if everything that begins to exist has a cause, then even the universe must also have a cause, because it must have had a beginning in the FINITE past. It could not have existed forever into the past, or else it wouldn't be here.
But if it is required that the universe began to exist, the cause of the universe must be something outside the universe, right? A thing cannot cause itself, that's absurd - that would mean it already existed before it exists to bring itself into existence!!
We have to have what Aquinas called a PRIME MOVER - a FIRST CAUSE. And if that cause was outside the universe, then we may infer some things about it. It was enormously powerful, because it had to be greater than the universe. An effect cannot be greater than it's cause. But it would also have to be immaterial because matter is a property of the universe. Another way of saying that is spiritual. It would also have to be timeless, since time is also a property of the universe. And space-less, again because space is a property of the universe.
Thus we arrive at a rudimentary definition of God! A timeless, space-less, immaterial, enormously powerful thing.
Now, this is where you can arrive at, just by THINKING about the universe and the question why there is something rather than nothing.
But science now gives this philosophical argument amazing support. First the 2nd law of thermodynamics says that all energy always goes from states of high order and concentration to low. In short, it says, everything is running down, entropy is a defining characteristic of the whole show.
This is true even if some parts of the universe temporarily increase in order and energy. Local increases in order always come at a cost to the whole amount of order. For example, if a goat is born from a single cell and grows up, that's an increase in order and concentration of energy. But this comes at a net loss of usable energy to the whole system, from the grass it ate, the air it breathed, and the sun energy it took to fuel all this.
In fact, the universe is running down, like a car running out of gas. If it had been here forever, there would already be no stars and no galaxies, because all suns, all galaxies are petering out, expending themselves. Even as new stars form from old ones, the whole show is gradually losing usable energy until it ends in what they call the "heat death": All matter/energy one uniform low temperature, everything dead.
But everything is not dead, so there had to be a beginning a finite time ago.
Of course the most powerful scientific evidence for a beginning is the Big Bang model. And here we have the most stunning physical proof that the universe had a beginning in the finite past. The proof was in the discovery of the expansion of the universe and cosmic background radiation, both testifying to the "Singularity" - a point of almost infinite density and energy, in the finite past, out of which all things exploded into the 13 billion light year monstrosity we measure today.
But there's one thing more: not only can we infer a timeless, spaceless, immaterial cause for the universe, we can also infer that this cause is personal. Here's why:
Before the universe, there was truly nothing around, not matter nor the laws matter runs by. NO THING. But nothing comes from nothing. So without matter or laws around to cause things to happen, if something did happen (and we're here so something really did happen out of nothing!) it would have to have been FREELY caused. But the only source of truly free agency we know of, is a person.
Therefore, the First Cause must be personal, because it wasn't acting due to the force of natural law or "have to" - It was acting based on "want to", and only persons do that.
So the maxim "nothing comes from nothing" turns out to be true. There is powerful "non-faith based" evidence for a very grand SOMETHING, and both philosophy and science hint strongly at the qualities of that SOMETHING, which sound very much like what we call "God".
Kalam Cosmological Argument
2. THE EVIDENCE FROM DESIGN
The fine-tuning of the fundamental properties of the universe is off the charts uncanny. Without this immaculate, exquisite fine-tuning there could be no stars, and none of the physical context required for life. So there has to be a reason for this precision.
Options include, either chance, law or design. There's no good reason to believe we could get that lucky by chance (multiverse theories notwithstanding), and there's no law above the other laws causing them to be so improbably precise. The only other option then, is that they were designed, which is exactly how they appear.
3. THE EVIDENCE FROM MORALITY
Objective moral values are something everyone, everywhere implicitly and explicitly believes exist. But if God does not exist, then neither do these objective values. If God does not exist, moral values are rather subjective and relative to different cultures and times and derived from chemical and social evolution and have no real demand on us.
But no one actually lives this way. Everyone (except psychopaths) acts as if they ARE bound to behave in certain ways that are good and avoid other behaviors that are bad. And not merely for expedience sake, for often the bad is rejected even though it is much more expedient!! Law then requires a ground in a Law Giver, thus the universal moral urge is powerful evidence for God.
4. THE EVIDENCE FROM JESUS
Jesus was crucified because he made the stunning claim that he was the long awaited Jewish Messiah. But more so because he claimed that as Messiah he was the Son of Man, divine figure of Daniel's prophesy and further, that he would rise from the dead. So if he did rise from the dead, this is powerful vindication of his claim to be God and evidence for God's existence.
The record of history (not assuming the Bible is 'inspired' but treating it as another ancient source) shows us 4 unavoidable facts about Jesus final days. These events are agreed to by most scholars, believing and skeptical: Jesus was crucified under Pontius Pilate and interred in a known grave. Jesus grave was found empty. Jesus disciples experienced what they claimed were appearances of Jesus alive after his crucifixion. Jesus disciples believed and proclaimed that they saw Jesus come back from the dead. There is only one theory that captures those facts into a coherent explanation: Jesus actually rose from the dead.