"Why Doesn't God Just Prove He Exists?"

A common argument from atheists is, just as the title reads, "If God exists, why doesn't He simply prove it?" Funnily enough, this is actually answered in the Bible itself.

In Mark 8, the Pharisees demand a sign of Jesus (Then the Pharisees came and began to argue with Jesus, testing Him by demanding from Him a sign from heaven. Mark 8:11). The following verse answers the atheists' hypothetical:

And he sighed deeply in his spirit and said, "Why does this generation seek a sign? Truly, I say to you, no sign will be given to this generation." Mark 8:12 ESV

What has happened here is that Jesus, being fully human and fully God, is keen to the Pharisees and acutely aware that they have already denied many signs and would certainly not respond to another. The sign would be wasted. Despite the multitude of signs they had already witnessed, they demanded a sign of Jesus.

"A generation incapable of appreciating such demonstrations shall not be gratified with them." - Jamieson, Fausset and Brown Commentary

Why would Jesus give a sign to a group of people who had already witnessed such miraculous signs and ignored them? They would not be satisfied with any sign Jesus had produced, as He has already produced multiple and they ignored them. They will not believe regardless. You must be open to seeing the miracles of the Lord for them to have any meaning or value to you. If you would ignore them anyway, you don't deserve them. Do not be surprised that unbelievers do not witness miraculous signs. Why ask God, "if You are real, give me a sign," if you would ignore that sign when it was given? You may think "oh I'd certainly believe God existed if He reached down from heaven and smacked me in the face!" but you would not, because your disbelief is emotional in nature. You refuse to believe in God not because there is no evidence but because you have rejected the evidence. Plentiful signs have been given already and you've denied them all. God does not "simply prove He exists" because He has already, and you've ignored it.

Further reading of interest lies in Luke 16:19-31, the parable of Lazarus and the Rich Man. The rich man in hell pleads to Abraham to allow him to warn his brothers of the perils of eternal damnation, where the final exchange takes place in verses 29-31:

“But Abraham said, ‘They have Moses and the Prophets; let them hear them.’ “But he said, ‘No, father Abraham, but if someone goes to them from the dead, they will repent!’ “But he said to him, ‘If they do not listen to Moses and the Prophets, they will not be persuaded even if someone rises from the dead.’”

Here Abraham contests that the rich man's brothers have all the testimony they need to understand and heed the words of the prophets, but they deny it. They would not be persuaded by any more "signs".

God's word contests further that we have all the evidence we need.

For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. Romans 1:20

Further, asking God to "prove He exists" as a nonbeliever is testing the Lord (as it was when the Pharisees tested Jesus in Mark 8:11), which He surely does not appreciate: "You shall not put the LORD your God to the test, as you tested him at Massah." Deuteronomy 6:16

How did they tempt Him in Massah? By raising the unbelieving question, “Is the Lord among us, or not?” - Ellicott's commentary for English readers

In Massah, humans attempted to test the Lord our God by asking Him to prove His presence, which is what the unbeliever does when they posit this argument.

You must be sincere in your prayers and without pride or spite if you wish to ask the Lord of any miracle - humble and genuine. God will not be tested by an unbeliever, to give a miraculous sign to one who asks in unbelief and scorn. God may choose to answer genuine prayers of the faithful and sincere. Faithful people who pray to the Lord are not testing Him, as they know God is capable of such miracles. They know God does not need testing because He is capable of infinite amounts of anything and everything. This is why it is said, James 1:6 "But let him ask in faith, with no doubting, for the one who doubts is like a wave of the sea that is driven and tossed by the wind."

The unbeliever and the doubter both receive the same response from the Lord, as the problem is the same - the unbeliever is the doubter. The doubter is the unbeliever. They are the same. If you believe you are faithful, but doubt the Lord can answer your prayers, you are no better off than the unbeliever. God is the Maker of Heaven and Earth, the Creator and Lord of all. It is not wrong to have doubt at times, it is a struggle we all have periodically (or even very often), but if we pray with doubt and ask of the Lord while simultaneously believing He cannot perform our request, we will see no signs. Doubt is a temptation and can be overcome, refusal of God's plentiful signs is a choice and you can choose differently.

If you will not believe the Lord when he answers you, He will not answer you.

Further reading here.