Salvation means to be forgiven and delivered from sin. When a man is saved he is delivered from sin. Salvation means to be saved from something. So when a man is saved he is saved from God's impending judgement. Man would not have been saved without the righteousness of God. We needed the righteousness of God to be saved. Without the righteousness of God nobody can be saved.
2 Corinthians 5:21 - For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
No man or woman on earth has the ability to save himself or herself. The righteous requirement of the law was fulfilled by Jesus Christ when he hung on the cross and the righteousness of God was credited to our account. When we got saved God's righteousness was put into our account. God's righteousness is the principle by which God works. Whenever God works he must work according to righteousness.
Whenever a man comes to the Lord his sins are forgiven and the righteousness of God is credited into his account instantly. We are saved by grace and are privileged to be made the righteousness of God. We can tell religion is genuine if God's righteousness is been put in us because it is an essential for our salvation.