A frequent argument proclaimed by atheists and agnostics is: "There is no proof of God. Show me some proof."
There are many answers to this. I will discuss two in this post.
First, such non-believers do not want to know the truth, so they simply deny the obvious. This has been true ever since the first men walked the earth.
It was true when the Israelites wandered in the desert; one minute in the presence of God, the next minute seeking their own solutions.
It was also true during the life of Christ that men denied who He was.
In Matthew 12:38-45, Jesus talks about those who see Him in the flesh, hear His words, witness His miracles, and still refuse to believe because He would not show them a sign when they demanded one. Christ said to them,
"An evil and adulterous generation craves for a sign; and yet no sign will be given to it but the sign of Jonah the prophet; for just as Jonah was three days and three nights in the belly of the sea monster, so will the Son of Man be three days and three nights in the heart of the earth."
What Jesus meant by this was that He would not be commanded by them, to show the particular sign that they wanted to see. He is God, not the sinner. He is not slave to the sinner, desperately hoping and waiting to be called upon to demonstrate His abilities. Instead, He says, He will demonstrate His divinity according to His timing, according to His plan. Amazingly, He lets them know exactly what to look for as The Sign: His resurrection from the dead.
Secondly, mankind already has many facts, many signs and many wonders that are certain proof of God's existence, they simply choose to deny them. Here are just a few:
1) Creation demands a Creator. Otherwise you must believe that nothing, with no cause, created everything in an orderly way. Not just animals, but space, time, dust, rocks, water, DNA, order itself, laws, mathematics, gravity, and on and on.
2) Evil demands God. What? Yes, I said that correctly. Here is how: You agree that there is evil in the world? Of course you do. But, how can there be evil unless we agree that there is a standard of good outside your opinion and my opinion? This standard of good must be something other than human, or the opinions of good and evil would vary widely, but they do not. This means there must be a Moral Law Giver who transcends humanity, and established the standard for 'good'. This Moral Law Giver is God.
3) The Bible. OK, I can hear some readers moaning already. You will argue, "You can't prove the existence of God by using the Bible." Why not? Can't I use the symphonies of Bach as proof that he was real, or the writings of Benjamin Franklin as proof that he was real? Of course I can, and therefore I can use the Bible, which claims to be the Word of God, as proof that God exists and caused the Bible to be written down.
4) The resurrection of Christ. Some will immediately say, "But there's no proof of that." Oh, yes, there is. First of all, eyewitness testimony is documented in the Bible (there were over 500 witnesses). Non-Biblical sources from contemporaries also establish that something quite unusual happened in Jerusalem after the crucifixion. They Jews, who tried to end the worship of Jesus, could not produce a body. In addition, the followers of Christ, who scattered widely during His trial and crucifixion, came back - bold and certain of their faith. Finally, the resurrection was such a momentous event in human history that the calendar suddenly changed.
These are just a few of the many proofs of God's existence. The most personal, however, is your conscience.
The word conscience means 'with knowledge'. You know that you have violated God's moral standard (the Ten Commandments) every time you stop and think about them.
Consider: how many lies you have told in your life, how many times you have been unjustly angry with others, how many times you have used God's name in a casual or disgusted way (this is blasphemy), or how many times you have taken something (regardless of value) that did not belong to you? If you have done each, you are a liar, a murderer at heart, a blasphemer, and a thief in God's eyes (and these are just four of the Ten Commandments). You know this is true because God placed the knowledge of His absolute good moral code inside you. Your conscience, which is right now telling you that these are wrong, and that (absent salvation) when you stand before Him on Judgement Day, you will be guilty.
You know it by how you feel: ashamed, perhaps embarrassed, convicted. You also know that guilt demands punishment, and the Bible tells us that the punishment for sin is eternity in hell.
If that concerns you, then you should also know that Christ died on the cross, and was resurrected three days later, just as He said He would, as a sign to you and all of humanity that He is the only way of salvation from the coming judgment. Once you understand this, you need do only two things: repent, and make Christ your Lord.
Repentance means to stop in your tracks, recognize that you are a sinner, that you are tired of a lifestyle as a rebel. You are ready to conform to God's desire: To seek after God; To live for God.
Making Christ your Lord means that you will pray to Him, read His Word (the Bible), and obey His commandments. You recognize that He is in charge and that you are ready to allow Him to control your every thought and deed.
If you are ready to repent and surrender, then cry out to Him in prayer. He will hear the prayer of the repentant. Then, read your Bible and do what it says. Find a local church (you can get help here or here). Living Waters also has some material that may help: Save Yourself Some Pain.
Men frequently deny the obvious. The Bible foretells that although men deny God's existence, they will have no excuse on Judgment Day:
"For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse." Romans 1:20
The time to stop denying is now.