We do not have to prove to the atheist that God exists. He intuitively knows that God exists but willfully suppresses the truth (see Rom. 1:18). Every person has a God-given conscience, which is the “work of the law written in their hearts” (Rom. 2:15). Just as every sane person knows that it is wrong to lie, steal, kill, and commit adultery, he knows that if there is a moral Law, then there must be a moral Lawgiver.
In addition to the testimony of his impartial conscience, the atheist also has the testimony of creation. It declares the glory of God, His eternal power, and divine nature, so that the person who denies the voice of conscience and the voice of creation is without excuse (Psa. 19:1; Rom. 1:19–21). If he dies in his sins, he will face the wrath of a holy Creator, whether he believes in Him or not.
This is why I don’t spend too much time trying to convince anyone that there is a God. To do so is to waste time and energy. What sinners need is not to be convinced that God exists, but that sin exists and that they are in terrible danger. The only biblical way to do this is to go through the moral Law and explain that God considers lust to be adultery and hatred to be murder, etc. It is the revelation that God is holy and just, and sees the thought-life, that convinces us that we are in danger of eternal damnation. That is what sinners need to hear to send them to the cross for mercy. So never be discouraged from preaching the gospel, and don’t get sidetracked by rabbit-trail issues that don’t really matter.
Psalm 97:6 The heavens declare His righteousness, And all the peoples see His glory.