I am perplexed by the fact that you can expound upon the idea that all man is born sinless.
I am afraid that you need to complete the chapter in Ezekiel 18 - where God says He invites us all to repent, after which He can give us the Holy Spirit which provides us with a new nature, which can avoid sin. We are all sinful. Every baby is born self-centered, which is sinful. Your commentary is misleading, as we are sinful in the womb – Psalm 51:5 "Behold, I was brought forth in iniquity,and in sin did my mother conceive me." Pretty straightforward there: conceived in sin.
We are sinners until we receive the Spirit of God at conversion. Jesus Christ would have not been the only sinless man otherwise. There would have been some who died at birth who would not have had the chance to sin.
"Truly, this only I have found: that God made man upright, but they have sought out many schemes" (Ecclesiastes 7:29).
Thus we learn that people are born sinless, but become sinful as they grow up. This truth is further emphasized by Ezekiel 18, which you ignored. In the first part, God shows that sin is an individual's responsibility. He summarizes His points by stated, "The soul who sins shall die. The son shall not bear the guilt of the father, nor the father bear the guilt of the son. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself" (Ezekiel 18:20). Since a son cannot inherit the guilt of his father, Seth did not inherit the guilt of Adam. Sin is not passed on genetically.
The root of your difficulty is a denial of what is sin. "Whoever commits sin also commits lawlessness, and sin is lawlessness" (I John 3:4). Sinfulness is a state reached when an individual breaks a command of God.
The Bible teaches that, outside of Christ, all men sin. This is not because we are born already in a sinful state. The Bible teaches by a simple declaration that everyone ends up breaking God's law. "Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned -- for until the law sin was in the world, but sin is not imputed when there is no law. Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come" (Romans 5:12-14). Death did not spread through mankind because everyone inherited Adam's sin, it spread because everyone, independently, has sinned. We know that Adam's sin was not spread to every because Paul said some did not sin as Adam did.
Your statement about God inviting repentance in the last portion of Ezekiel 18 is correct, but no where does this chapter mention the giving of a new nature. This is something that you added. Nor does this section teach that a repentant sinner can avoid sin. Actually it warns about the opposite. "But when a righteous man turns away from his righteousness and commits iniquity, and does according to all the abominations that the wicked man does, shall he live? All the righteousness which he has done shall not be remembered; because of the unfaithfulness of which he is guilty and the sin which he has committed, because of them he shall die" (Ezekiel 18:24). Like the Letter to the Hebrews, God is warning people that they must choose to remain faithful. "Beware, brethren, lest there be in any of you an evil heart of unbelief in departing from the living God; but exhort one another daily, while it is called "Today," lest any of you be hardened through the deceitfulness of sin. For we have become partakers of Christ if we hold the beginning of our confidence steadfast to the end" (Hebrews 3:12-14).
Psalm 51:5 states, "Behold, I was brought forth in iniquity, and in sin my mother conceived me." David says he was born in sin and that his mother conceived him in sin. It does not say that David was sinful. David is weeping over why he had fallen into sin. He states that he was born in sin -- that is, he was born into a world of sin. He states that he was conceived in sin -- that is that he was conceived in a sinful world. He attributes the evil influences of the world, present from the time of his conception, in pulling him into the trap of sin. Such is state by James, though not to such an extreme. "Let no one say when he is tempted, "I am tempted by God"; for God cannot be tempted by evil, nor does He Himself tempt anyone. But each one is tempted when he is drawn away by his own desires and enticed. Then, when desire has conceived, it gives birth to sin; and sin, when it is full-grown, brings forth death. Do not be deceived, my beloved brethren" (James 1:13-16). To say people are born sinful is to say that God made me sinful -- something that James says God does not do. Sin comes from individual choice in following the temptations of the world.
While you focused on Psalm 51:5, you ignored Psalm 22:9-10, also written by David, "But You are He who took me out of the womb; You made Me trust while on my mother's breasts. I was cast upon You from birth. From my mother's womb You have been my God." You stated that people need to be converted and receive a new nature from God before they can lean upon God, but David states that he trusted God from his birth and even before, while he was still in the womb.
The statement that only Jesus was without sin is naturally qualified as among those who lived past the age to be accountable for sin. Are you saying that children who die are in hell? Those whom the Lord said, "Assuredly, I say to you, unless you are converted and become as little children, you will by no means enter the kingdom of heaven" (Matthew 18:3)? If children are born sinful, then why do we speak of the innocence of childhood? We do this because we know that children are innocent. "Moreover your little ones and your children, who you say will be victims, who today have no knowledge of good and evil, they shall go in there; to them I will give it, and they shall possess it" (Deuteronomy 1:39). The phrase "knowledge of good and evil" is exactly the same one attributed to the Tree of the Knowledge of Good and Evil. Children are just like Adam and Eve before they partook of the forbidden fruit -- made upright by God until Satan lures them away into the sins of the world.