We'll start with the obvious: If there existed a definitive, inarguable proof for the existence of God, there would be fewer atheists in the world.
That said, God's existence is something you can be sure about in your own life. Books like Lee Strobel's The Case for a Creator: A Journalist Investigates Scientific Evidence That Points Toward God or Michael Behe's Darwin's Black Box: The Biochemical Challenge to Evolution explore the stunningly intricate world in which we live, pointing out the statistical impossibility of the universe existing by chance or life evolving on its own. The perfect interaction between natural laws such as gravity and electromagnetic force suggests an Engineer with a flawless understanding of how to design an entire universe, and the continuous discoveries in all fields of science remind us that we have barely begun to scratch the surface of the complexities and mysteries of our world.
Three carefully researched free booklets Does God Exist? , Creation or Evolution: Does It Really Matter What You Believe? and Is the Bible True? can help you weigh the evidence and see for yourself the answers to the challenging questions posed by atheists and evolutionists. These booklets show how the existence of matter, the existence of life and the record of fulfilled prophecies help prove God's existence.
All this aside, belief in God eventually comes down to a matter of faith. You can study all the evidence in the world for God's existence, but clever minds will always be able to produce a tempting justification for doubting.
If you wish to be sure—absolutely sure—that there's a God, pray to Him. Ask Him to help you to see His fingerprints in your life and understand His plan for you. He makes a promise to those who diligently look for Him—a promise just as relevant today as it was when it was made thousands of years ago: “And you will seek Me and find Me, when you search for Me with all your heart. I will be found by you, says the Lord” (Jeremiah 29:13-14 Jeremiah 29:13-14 13 And you shall seek me, and find me, when you shall search for me with all your heart.
14 And I will be found of you, said the LORD: and I will turn away your captivity, and I will gather you from all the nations, and from all the places where I have driven you, said the LORD; and I will bring you again into the place from where I caused you to be carried away captive.
American King James Version×).
There is a God. But the only way you can find absolute proof is to seek Him yourself.