8 And when He has come, He will convict the world of sin, and of righteousness, and of judgment: 9 of sin, because they do not believe in Me; 10 of righteousness, because I go to My Father and you see Me no more; 11 of judgment, because the ruler of this world is judged.
John 16:8-11
The Bible is clear that the SIN of the world is unbelief in Christ. All the other sins that a non-Christian commits is not what is keeping them from a relationship with God. In fact, if they are attempting to attain God's righteousness by their own works then they are nullifying what Christ did on the cross for them!
Just as the nation of Israel was trying to pursue righteousness by law-keeping, they did not receive the righteousness of God.
That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith; but Israel, pursuing the law of righteousness, has not attained to the law of righteousness. Why? Because they did not seek it by faith, but as it were, by the works of the law.
Romans 9:30-32
So unbelievers need to repent of their UNBELIEF in Christ for Salvation, just as John the Baptist stated "The time is fulfilled, and the Kingdom of God is at hand. Repent, and BELIEVE the gospel." (Mark 1:15)
Just as Paul said to the Philippian jailor when he was asked, "Sirs, what must I do to be saved?" So they said "BELIEVE on the Lord Jesus Christ, and you will be saved, you and your household." (Acts 16:30-31)
And Jesus Himself says, "Most assuredly, I say to you, he who BELIEVES in me has everlasting life." (John 6:47)
8 For by grace you have been saved through faith, and that not of yourselves; it is the gift of God, 9 not of works, lest anyone should boast. 10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them.
Ephesians 2:8-10