Abraham must not have been justified by works, else he would have had something to boast about. If he had done the works, he would have earned justification as wages by his works, but Scripture says he believed, and that faith was reckoned as righteousness to him. To the one who does not work but believes in Him who declares righteous the ungodly, his faith is reckoned as righteousness to him, like Abraham, and like David (Psalm 32:1-2). David's sins and lawless deeds, rightly credited to him because he committed them, were forgiven, covered, and not counted against him. The Lord would be unjust in doing this if the penalty for those sins was not paid. And with what righteousness were the sins covered? With Christ's. In the gospel, the righteousness of God is revealed from faith for faith, while the wrath of God is revealed from heaven (from God) against all unrighteousness and ungodliness. For those who believe, who are as ungodly as those who receive the wrath of God, the wrath they deserve is put on Christ and their ungodliness is covered by the righteousness that they receive by believing in Christ.
Now, is the forgiving, covering, and not-counting a blessing reserved only for the circumcised? Certainly not, for Abraham was counted righteous by faith before he was circumcised, because he received circumcision as the seal of the righteousness already credited to him. Therefore, his example is proof that the uncircumcised can know the blessing of having sin forgiven, covered, and not counted to them because Abraham himself was uncircumcised when he was justified. So then he is the father of all who are justified, both of those who are circumcised in flesh and in heart and of those who are not circumcised but believe. He is the father of those who have a righteousness apart from circumcision, and the father of those who have circumcision but more importantly walk in the footsteps of the faith that Abraham possessed before he was circumcised.
For the promise to Abraham that he would be the father of nations (heir of the world) did not come through the law but came before it was given; it came through the righteousness of faith, not the righteousness of the law. Faith is invalidated, nullified, and the promise void if the inheritance of nations is by works of the law, not faith. You can sin in falling short of the glory of God and love of Him, even if you know nothing of the law and therefore have not deliberately transgressed ordinances, trespassed the boundary. The law, apart from grace, only brings knowledge of sin, and sin increases the more the mind and heart enslaved to sin knows of the law; the law thereby brings wrath, for apart from being righteous by faith there is nothing we can do as sinners but receive the condemnation of the law and face the wrath that we deserve. Under the inevitability of wrath under the law, if the promise came through the law, it would not only be void for the Gentiles who do not have the law, but also void for the Jews because of the impossibility of salvation through works of the law: an empty promise.
But salvation rests in faith on Christ, not in works on us, so the promise is sure and the righteousness of faith is a Rock beneath our feet, and with the Almighty doing the heavy lifting (so to speak), how could the promise of Abraham being the progenitor of all the faithful fail to come to pass? It must depend on faith, for then the promise rests on the grace that God shows in giving faith and in justifying through that faith both Jew and Gentile, those who keep to the law but share the faith of Abraham, not trusting in a righteousness that comes by their own law-keeping but by that righteousness that comes apart from works of the law, by faith; and those who have not the law, like Abraham, yet believe, to whom also is counted righteousness.
In hope Abraham believed against hope; that is to say, in trusting in the surety of God's promise, Abraham believed against the kind of hope that trusts in natural process and that fails when confronted with the frailty and futility of man. He believed that he should become the father of many nations, as he had been told, "So shall your offspring be." He did not weaken in, did not waver in unbelief, but grew strong in his faith because he was fully convinced that God was able to do what He had promised, and this was counted to Abraham as righteousness. This faith of Abraham is counted as righteousness and is the same as the faith through which the perfect righteousness of Christ is reckoned to us not just because the only righteousness by which anyone is ever justified is Christ's but also because the faith that Abraham had and the faith that we have are identical: both consist in a rock-solid, dogged, unwavering trust that God will be faithful to keep His promises despite all factors suggesting otherwise, both the promise to make Abraham the father of many nations and the promises that "the righteous shall live by faith," "the seed of the woman would crush the head of the serpent," "the servant of the Lord would bear the sins of the ungodly and heal their sin-sickness with His wounds," etc. No matter how small, faith given from God perseveres, persists, and presses on in trust.
This counting of Abraham's faith in the faithfulness of God to keep His promises, no matter how impossible they seemed, was recorded for our sake so that we might know with assurance that it will be counted to us as righteousness who believe in the faithfulness of God who raised from the dead our Lord Jesus Christ, who was pierced for our transgressions, slain for our sins, and was raised for our justification, that we would receive the blessings that David spoke of: sins forgiven, unrighteousness covered, transgressions not counted against us but laid on Christ, and righteousness declared over the sinner.