The word used in the scripture regarding the matter of the first humanity, the removal of the first humanity, the release from law, and the eradication of sin is 'reconciliation' (commonly so stated, though I prefer 'restoration' myself as it is not a matter of emotional 'reconciling' but a matter of restoration under Headship). The words in Greek are katallasso and apokatallasso.
The matter of sin is dealt with in Christ and in his death.
See Romans 5:12-21 for example. Sin itself is eradicated in Christ when he was 'made sin'. 2 Corinthians 5:21.
Thus made sin (or 'effected' sin, as it is poeio make/do) he died, taking sin itself down into death. Our old humanity is crucified with Christ. The removal of the sin of the world is a doctrinal matter, not a matter of Christians 'not sinning'.
'But now we are delivered from the law, that being dead wherein we were held ; that we should serve in newness of spirit, and not in the oldness of the letter', Romans 7:6.
God, sending his own Son in the likeness of sinful flesh and about (it is peri) sin, condemned sin in the flesh, Romans 8:3. Here, Paul describes the Son coming both in the likeness of sinful flesh (his incarnation) and 'about' sin, that is to say, being 'made' (or 'effected') sin - see 1 Corinthians 5:21 - sin itself was associated with him (though he were sinless) in the sight of God.
In death, that sin was taken into death, and was no more, It was eradicated. That is to say the 'sin of the world' for 'Behold the Lamb of God who taketh away the sin of the world', John 1:29. He takes it away, himself. (It is not taken away by the deeds of others).
This is what is revealed by the brasen serpent, John 3:14, in the wilderness. They did but look and they were healed from the plague, the biting of the serpent, Numbers 21:9.
All we have been bitten by the serpent. All have gone astray. Sin is within all of us.
Nor can we eradicate it by our own holiness. Paul discovered this as he tells us in Romans 7 - he had no power over sin as long as he was under law. For the law is the strength of sin, 1 Corinthians 15:56.
The harder one fights, the stronger it becomes. O wretched man that I am ! cries the sinner under law, Romans 7:24.
But God be thanked, there is a Deliverer - 'through Jesus Christ my Lord'.
For He is the One who takes away the sin of the world.
Behold the Lamb of God, is all that is required, just as they in the wilderness did but look at the serpent that was lifted up as an 'ensign'. So was the Son of man lifted up and so shall they that look upon him live, and be delivered from sin that dwells in flesh.