If you talk to an atheist about God, they will almost always ask for evidence that He exists. On its own, this is actually quite sensible. Healthy skepticism is a good thing, and I actually wish atheists would apply it more often. If they would only apply the same level of skepticism to Evolution, for example, they'd be a lot easier to reach with evidence for God.
But providing evidence for God isn't as easy as providing evidence for a rock. If I claim to have a rock in my pocket, I can prove it to you without even taking it out. If I do take it out, that's even more proof. If I let you examine it, you have the ability to use all 5 senses to observe the rock. Thus, you would need to set your skeptometer to maximum to deny the existence of the rock.
But other claims about the rock are less up to observation, particularly regarding the history of the rock. If I was to tell you, for example, that I picked the rock up from Echo Beach on the 12th of October 2019, none of that would be provable. I can make a case, but you can't see, hear, smell, taste, or touch the past. My testimony, as the rock's owner, is all you have to go on.
Currently, God is towards the more intangible end of the spectrum. You can't bottle Him up, stick Him under a microscope, observe Him through a telescope, measure Him with scales, or anything like that. Proving God exists requires some different forms of arguments.
For many atheists, this is already a problem. Objectively, "I can't see God, therefore He doesn't exist" is as silly as "I can't see air, therefore it doesn't exist". But many atheists insist on a number of equally silly tests for God, and they refuse to believe in Him until they are fulfilled.
One common argument for God's existence is the moral argument. The moral argument is fairly simple:
P2: Morality exists.
C: God exists.
This is a fairly solid argument, though it is often misunderstood. Almost every response depends on some misunderstanding or other. But taking the argument as it is, it is nigh irrefutable. The conclusion necessarily follows from the premises, so the only way an atheist can dispute the argument is to dispute the premises.
While some atheists are consistent, and will happily admit that, in their worldview, there is no such thing as morality, most atheists - and indeed, most people - admit that there is an objective standard by which every aspect of human behavior must be judged. But the problem for atheists is that they neither agree on that standard, nor do they have foundation for doing so.
When two Christians disagree on morality, the fix is fairly simple. We both agree that the Bible is the infallible word of the Living God, so we look to it. For example, imagine a disagreement on the morality of taxation. This Christian thinks taxation is theft, that Christian thinks it's reasonable for the government to require a certain fee for services rendered. What do we do? We turn to Romans 13, and right there, in the first 7 verses, it tells us we should pay taxes to the government because they are ministers for the punishment of evil, and refusing to pay them for this service is rebellion against God.
This is not a difficult concept. When two Christians disagree on morality, there are only three possible problems: Lack of knowledge (one doesn't know what Scripture says), lack of faith (one doesn't actually believe the Bible, or may even believe an extra-Biblical source), or lack of will (one doesn't want to obey God). The presence of one or more of these three will inevitably result in division, but the division can be fixed by removing these three elements.
But when atheists disagree on morality, there is, and can be, no such simple fix. Morality is an inherently religious concept, and is completely abstract. Therefore, when one atheist makes a claim about morality, any other atheist can say those two little words, "prove it". Then, they simply use the exact same resistance techniques they use to reject the arguments for the existence of God.
What can they do to resolve the dispute, at this point? They have no Scriptures to appeal to. No higher power to submit to. It's just atheist vs. atheist, arguing about things that are exactly as tangible as the God upon whom, ultimately, morality is based. That means if you are skeptical about God, you must be exactly as skeptical about every moral belief you hold.
Now, that does not mean you can't hold them anyway. Hypocrisy is human nature, consistency within a belief system is not essential. So you can hold moral beliefs within a belief system that has no grounding for them. But mere belief is insufficient, not to mention entirely unconvincing.
So, first, I'm going to take the classical approach to the moral argument. It's simple: If you believe in morality, the logical extension is to believe in God. There just isn't a sensible way around this (though atheists have certainly tried).
But I also want to put a twist on the moral argument. Not only does the existence of morality necessitate the existence of God, but as God and morality are both intangible, the same standards must apply to both. If you don't need to scientifically prove morality, you don't have to scientifically prove God. Other arguments must lead us to morality, therefore other arguments for God are also valid.
Of course, atheists can make all of this go away by just admitting that morality doesn't exist in the worldview they have chosen. But who wants to be in the position of knowing certain things are morally wrong, but having to confess that really, in one's own worldview, they're just morally different? "I'm personally not into rape, but Bill over here thinks it's totally cool. To each his own I guess." When a "good person" has to admit his worldview makes him morally equal to history's most notorious villains, they tend to get uncomfortable. For obvious reasons, but also theological ones.
According to Scripture, "...Gentiles, who do not have the law, by nature do the things in the law,..." (Romans 2:14). God has given us moral instincts, and so even as sinners, we have a conscience that allows us to recognise good and evil. This removes all excuses. We can, for sake of rejecting God, acknowledge that if there is no God, there are no rules, then proceed to deny that there is a God. But instinctively, we know that there are rules. Therefore, that denial is just one more way of breaking them.
It is also the best way to ensure we are never forgiven for breaking them. As it stands, God does have sufficient mercy to forgive sin. In fact, while our sin makes even our righteous acts comparable to filthy rags (Isaiah 64:6), God is willing to reward them as if we'd never sinned. But there is a "catch".
See, God is good. He cannot just let evil slide. Therefore, there must be payment for sins. Enter the Lord Jesus Christ, Son of God, who was tempted in all things as we are, yet without sin (Hebrews 4:15). Nevertheless, He died a sinner's death, receiving the full wrath of God, so that all who confess Him as Lord and believe God raised Him from the dead will be saved.
By instinct, an atheist knows there are moral laws. By logic, we know that without God, there cannot be. By revelation, we know what those laws are, and also that we have broken them. By faith, we can receive a full pardon, even a reward, as if Christ were guilty of our sin, and we were righteous as He was.