But we are all born sinners.No, I don't believe anyone is born with a sin nature.
This quote is an excellent answer about sin nature.
Are we all born sinners? | GotQuestions.org
Humanity is totally depraved; that is, all of us have a sinful nature that affects every part of us (Isaiah 53:6; Romans 7:14). The question is, where did that sinful nature come from? Were we born sinners, or did we simply choose to become sinners sometime after birth?
We are born with a sinful nature, and we inherited it from Adam. “Sin entered the world through one man, and death through sin, and in this way death came to all people” (Romans 5:12). Every one of us was affected by Adam’s sin; there are no exceptions. “One trespass resulted in condemnation for all people” (verse 18). We are all sinners, and we all share the same condemnation, because we are all children of Adam.
Scripture indicates that even children have a sin nature, which argues for the fact that we are born sinners. “Folly is bound up in the heart of a child” (Proverbs 22:15). David says, “Surely I was sinful at birth, / sinful from the time my mother conceived me” (Psalm 51:5). “Even from birth the wicked go astray; / from the womb they are wayward, spreading lies” (Psalm 58:3).
Before we were saved, “we were by nature deserving of wrath” (Ephesians 2:3). Note that we deserved God’s wrath not only because of our actions but because of our nature. That nature is what we inherited from Adam.
We are born sinners, and for that reason we are unable to do good in order to please God in our natural state, or the flesh: “Those who are in the realm of the flesh cannot please God” (Romans 8:8). We were dead in our sins before Christ raised us to spiritual life (Ephesians 2:1). We lack any inherent spiritual good.