God Hides Himself
Have you ever tried to "prove" to yourself that God exists? Or doesn't exist? It's a waste of time.
Truly, You are a God who hides Himself, God of Israel, Savior! - Isaiah 45:15 (see also Isaiah 6:9-10, Matthew 13:10-17, Romans 9:14-18 etc.)
There is nothing wrong with trying to understand reality. Science and logic make sense, but they are limited. They depend on what our senses and what instruments can detect. But smart people have been trying to make sense of life for thousands of years, and there is still so much that we don't know.1 If we accept the possibility that a being can exist outside of time (Isaiah 46:10), we can imagine that any scrap of information about any type of detector would be known. So, that being could avoid being detected.
Sadly, tragically, many Christians have tried to "prove" that God exists. Nearly always, better science comes along and gives rebellious people an excuse to say that Christianity is foolish. Therefore, they think they can live in God's universe with no fear of consequences (Proverbs 1:7, Galatians 6:7-8).
It would be one thing for someone like a scientist to claim that God doesn't exist if that person lives a "perfect" life according to Christianity. Otherwise, there is the possibility that bias has crept in, and that scientist's personal life is influencing what is said professionally.
The problem with any "proof" of God's existence is that it can always be corrupted. Disinformation, deception, half-truths, proud claims of superiority, "both-sideisms" and outright lies (e.g. Genesis 3:4-5) - there is a lot of that going around right now. But if we might agree that believing in Him (John 3:16) would prevent rebellions for eternity, God does seem to know what He is doing. And God has every right to be selective about who He let's into His heaven.
At the same time, we know that God reveals Himself (Romans 1:19-20, Psalm 19:1-4). The Bible is the only known text to make significant and accurate predictions of the future (e.g. Psalm 22, Isaiah 53). Though some will deny everything, it is very hard to disagree that the Bible has been around for a very long time.2
At some point, it becomes difficult for a person not to believe. People are certainly prone to burying their head in the sand and covering their ears in the face of facts. In fact, it takes a lot of faith and trust in human intellect to believe in atheism.
1. It's easy to find ridiculous descriptions of reality, both in the ancient past and our armchair-scientist present. Even at the highest levels of science, and even though humans have studied everyday gravity since history began, we still don't know what it is. Likewise, we currently think that the universe is mostly made up of Dark Matter and Dark Energy, but we don't know what they are. So if we don't even know those things, how can we scientifically or logically say there is no God?
2. The Septuagint was a translation of the Hebrew Old Testament into Greek. There is widespread agreement that most of it was written about 250 B.C. Similarly, the Dead Sea Scrolls included copies of the Old Testament that were written about the time that Jesus was born. It is difficult to believe that the many prophesies in the Old Testament could be just chance.