“... even if you should suffer for righteousness' sake, you will be blessed. Have no fear of them, nor be troubled, but in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect, having a good conscience, so that, when you are slandered, those who revile your good behavior in Christ may be put to shame. For it is better to suffer for doing good, if that should be God's will, than for doing evil. (I Peter 3.14-17 ESV)
I can believe in the existence of God based on several things: creation around me, the life I have and the love in the world that resists the human urge toward being self-centered.
Creation is so diverse and expansive, that it takes more faith in my mind to disbelieve in a Creator than to believe in one. Can chance create a man? Can it create the massive jungles that thrive with living creatures? If I put a pig in a room with a pump and some laces will it develop into a football over a long enough time? These questions are obviously answered in a negative manner. The world is specially designed. Such a design requires a Designer. Our bodies are intricate machines that are more complex than a computer- indeed, to this day there are still many mysteries about the human body. Such a “machine” requires thought, design and skill to produce. This begs for a belief in a real, existing God.
The life I have, the understanding and ability to learn and grow intellectually, the ability to love- it all cries out as evidence that God has made me different from a mere developed organization of cells. We cannot recreate a human life. Cloning will never do so.
Finally, when we see love where the human soul cries out for revenge, hatred or racism, we see the influence of God. We are egocentric creatures. When we resist that egocentrism, we reflect the influence of a God who is love. Darwin proposed that evolution requires natural selection. God put love in men to instill natural protection- the protection of the weak by those who are stronger.
This is my briefest answer to the question “How can you believe the existence of God?