If you will allow me to intervene for a moment.
Let's not call it 'sin nature' for a moment and simply take a look at young children.
We have to teach them to share -- grabbing for oneself comes naturally.
We have to teach them patience -- wanting NOW comes naturally.
We have to teach them self-control (and some never learn it!)
etc.
This tendency to grab for oneself, to demand, to 'want what I want when I want it' is, in an infant and young child, part of their nature. It is what will become sin later, but Paul states very clearly in Romans that without the law sin is not taken into account. He states that the law defines sin for us and in Romans 7 that he was alive until he knew the law (since there is no reincarnation, we have to understand he meant spiritually alive, which means not separated from God).
Thus, being born with a sin nature simply means being born with the tendency to grab and do for oneself regardless of others.
Someone says they don't believe in morality, yet I will bet the house that said person will agree that young children should be taught to share, be patient, etc. Why? Because it is 'right.' That's morality -- what is right. We don't argue that such a thing as 'right' exists, just about what is right or not. Morality is there, despite the disclaimer.
Alpha, we cannot repent of having a sin nature. That is like asking me to repent of being born a woman -- as though I had anything to do with it! But when we know the law and then consciously and deliberately rebel against it, that is sin, and that must be repented of. The fact that we have rebellious natures from birth is not something we can be held responsible for. But the decisions we make later regarding how to deal with it -- that we are responsible for.
In the meantime, no one goes to hell because of sin. Jesus, we read in Hebrews 2, tasted death for everyone. EVERYone. All sin has been atoned for (which is different from forgiveness, by the way). So we read in John 3:16 and on that it is our belief in Jesus Christ which is the watershed point where salvation and damnation are concerned. Are we children of God, through faith (See John 1) or not?
We still need to, even as saved people (those of us who are born again -- which means we now have a new nature which does not have the tendency to sin and rebel...), confess and repent when we do sin. Being born again does not mean we don't sin, but it does mean we don't WANT to sin and refuse excuses for it. We want to please our Lord and are extremely sorry when we realize we haven't! Then God is faithful to forgive us, as John tells us in his first epistle.
Children, in the meantime, are not lost. None of them. It is not until they understand the law, as Paul tells us in Romans 7, that they die spiritually, or become separated from God. Jesus was the one time sacrifice for all, including the sacrifice for unknown and unintentional sins (which are part of the sacrificial system of the Old Testament). Thus the children are covered by His sacrifice no matter how young one wants to argue their actual sinning begins.