Rom 1.17 For in the gospel the righteousness of God is revealed—a righteousness that is by faith from first to last, just as it is written: “The righteous will live by faith.”
What set the Gospel apart from the Law was the fulfillment of Christ, who enabled righteousness to last, from beginning to end. Sin could not disqualify a man whose faith was in Christ, who knew no sin.
The Law contained all kinds of ways of mitigating sin so that a man and a nation could remain blessed by God and in fellowship with Him. But the sin nature remains within man, and the Law could not get past this disqualifying factor.
But the Gospel offered Christ as the ultimate mitigating factor which does overcome this disability. Faith in Christ enables us to pursue his righteousness continually, without disqualification, because his mercy never stops advocating on our behalf, restoring us continually to God.