The Bible says that God cannot deny Himself, which means that He cannot do anything that contradicts His nature. As Creator, God is the definition of reality. If God did something that contradicted His nature—for example, lying—He would be contradicting reality! Generally, when someone proposes something that God cannot do, such as create something so large that He can’t lift it, they are proposing something illogical. Such illogical fallacies must be rejected because people are not proposing them out of a desire to please or to know God better. Instead, they are proposing them as an act of rebellion against the reality of who God is and His future wrath against all unrepentant sinners. God will not be mocked, and every man and woman will get what they deserve, regardless of the excuse they make for not believing Him. So, yes, God cannot do anything that contradicts His nature. However, that does not limit His power. Instead, it shows that He is the unchangeable, infinitely powerful God that He claims to be!
Some claim God isn’t all-powerful by proposing illogical scenarios—like asking if He can create a rock so heavy He can’t lift it—but these “tests” ignore that God’s nature is more than just power and must be consistent with reality. Because His attributes are infinite and unchanging, He cannot do what is logically absurd—not due to weakness, but because nonsense is not a measure of true power. The main reason why skeptics propose a list of things that God can't do is to find a way the escape from His wrath. After all, if God is not all-powerful, then maybe He won’t be able to judge them for their sin. In other words, the tests aren’t really designed to know God better but to foolishly convince oneself that God does not exist.
However, all they prove is that the infinite, all-powerful, holy, and just God does not change and will not deny His nature to satisfy sinful creatures' whims. He hates sin now as much as He always has and will destroy it. Ironically, the one thing that would prove that God is not real would be if He could not judge sin. However, the Bible is clear that He is more than capable of doing that. Since He will do that in the future, He has provided a short time to escape that coming wrath. Denying God exists is not a permanent solution, it is a denial of reality (Romans 1:18–20), and it only increases His wrath against you (Romans 2:5)!
Instead, knowing that God is all-powerful in a way that is consistent with His nature, we are to be quick to repent of our sin and quick to cling to His one way of salvation. The Father sent His Son, Jesus, to do what we cannot do: be perfectly righteous. Only sinners are supposed to die (Romans 6:23), but Jesus willingly died in the place of sinners, accepting the Father’s wrath as if He had sinned. Take hold of that free gift (Romans 6:23b) and repent of your sins, confessing that His Son is Lord, and you will be saved (Romans 10:9–10).