Tim Keller’s 5 clues that point to the existence of God in his book The Reason for God:
Clue 1: The Mysterious Bang — Either God created the universe, or it “just happened” – and both require faith.
Clue 2: The Cosmic Welcome Mat — This clue is also called the anthropic principle (or fine-tuning argument), which recognizes that humans could not exist in any other universe than this one. If any of this universe’s constants were different, we would not be around to observe them.
Clue 3: The Regularity of Nature — Continued regularity is a matter of faith. There is nothing guaranteeing the universe will be here tomorrow, or that it will operate according to all the cycles we’ve been observing throughout the years, with all its laws.
Clue 4: The Clue of Beauty — “We may, therefore, be secular materialists who believe truth and justice, good and evil, are complete illusions. But in the presence of art or even great natural beauty, our hearts tell us another story. … regardless of the beliefs of our mind about the random meaninglessness of life, before the face of beauty we know better. … Isn’t it true that innate desires correspond to real objects that can satisfy them? … Doesn’t the unfulfillable longing evoked by beauty qualify as an innate desire? We have a longing for joy, love, and beauty that no amount or quality of food, sex, friendship, or success can satisfy. We want something that nothing in this world can fulfill,” (134-135).
Clue 5: We Trust Our Belief-Forming Faculties — The belief that all of our beliefs and values are naturally selected and not to be trusted—is not to be trusted. The fact that we do trust our belief-forming faculties is a clue to God.
This is an excerpt of the summary found in this post.