When Paul tries to convince the Romans that the Gentiles can be brought into the covenant family of God without first being circumcised or being subjected to the law, he uses Abraham as his example why. By Paul’s reasoning, Abraham was the original Gentile that God brought into the covenant and God considered him righteous not for his works or his circumcision or his following of the law (Abraham didn’t yet know about such things), but for his faith. Therefore, faith is the definition of salvation for Paul and Abraham is the earliest example of proof. Though the law is good and upheld by the Christian (for it has not been abolished), obedience of the law is now found in the obedience of the law’s ultimate interpreter, Jesus Christ, who has become the fulfillment of the law.
Therefore, we are saved by the same formula that God’s people have always been saved by throughout history: God’s grace given to sinners on behalf of their faith/faithfulness/belief/commitment/believing loyalty/allegiance to God. What has changed in this formula in the New Testament, however, is the crux upon which all of our faith now hangs: King Jesus Himself, who is the fulfillment of the original covenant made to Abraham, the forgiveness of sins, and the one who has paved the way for us to enter into the resurrection life of the new heavens and new earth, where we will live with new resurrected immortal bodies. We have been given evidence of all of this through the downpayment of the Holy Spirit, through which full resurrection will one day come, and has also already begun now inside of us. We can only receive these promises by our faithful allegiance to Jesus, for to be faithful to Jesus, is to be faithful to God—for Jesus is God-in-flesh.