What then shall we say that Abraham, our forefather according to the flesh, discovered in this matter? If, in fact, Abraham was justified by works, he had something to boast about—but not before God. What does Scripture say? “Abraham believed God, and it was credited to him as righteousness.” (Romans 4:1-3)

Paul is saying that if Abraham was justified or declared righteous because of his works or actions, he certainly had the goods to boast about it. But not in God’s eyes. Not in God’s economy, where righteousness, or right standing before God, is established by faith and trust in God, not works or actions:

Now to the one who works, wages are not credited as a gift but as an obligation. However, to the one who does not work but trusts God who justifies the ungodly, their faith is credited as righteousness. David says the same thing when he speaks of the blessedness of the one to whom God credits righteousness apart from works:

Is this blessedness only for the circumcised, or also for the uncircumcised? We have been saying that Abraham’s faith was credited to him as righteousness. Under what circumstances was it credited? Was it after he was circumcised, or before? It was not after, but before! And he received circumcision as a sign, a seal of the righteousness that he had by faith while he was still uncircumcised. (Romans 4:9-11a)

And so Abraham represents all people, Jews (circumcised) and Gentiles (uncircumcised) who are able to be declared righteous by God because of faith (belief in Jesus’ saving act), not one’s works:

So then, he is the father of all who believe but have not been circumcised, in order that righteousness might be credited to them. And he is then also the father of the circumcised who not only are circumcised but who also follow in the footsteps of the faith that our father Abraham had before he was circumcised. (Romans 4:11b-12)

No, it’s not adherence or obedience to the law or good works. And anyway, no one can keep the law and so will be judged by God; and those without the law (Gentiles) are not aware of any sin that would be exposed by the law:

It was not through the law that Abraham and his offspring received the promise that he would be heir of the world, but through the righteousness that comes by faith. For if those who depend on the law are heirs, faith means nothing and the promise is worthless, because the law brings wrath. And where there is no law there is no transgression. (Romans 4:13-15)

The Proof Point
To sum it up: the promise to Abraham was simply to be received and believed by faith, for everyone, given by God by grace as a gift. No one had to work for it:

Therefore, the promise comes by faith, so that it may be by grace and may be guaranteed to all Abraham’s offspring—not only to those who are of the law but also to those who have the faith of Abraham. He is the father of us all. As it is written: “I have made you a father of many nations.” He is our father in the sight of God, in whom he believed—the God who gives life to the dead and calls into being things that were not. (Romans 4:16-17)

As the father of the nations (Jews and Gentiles), Abraham believed what God was going to do, in spite of the odds or his and Sarah’s old age condition.

Against all hope, Abraham in hope believed and so became the father of many nations, just as it had been said to him, “So shall your offspring be.” Without weakening in his faith, he faced the fact that his body was as good as dead—since he was about a hundred years old—and that Sarah’s womb was also dead. Yet he did not waver through unbelief regarding the promise of God, but was strengthened in his faith and gave glory to God, being fully persuaded that God had power to do what he had promised. (Romans 4:18-21)

And Paul stresses that this crediting of righteousness applies to all of people, then and today, who believe that Jesus was/is Lord and raised from the dead, solely to account (atone) for our sins and be justified by God.

This is why “it was credited to him as righteousness.” The words “it was credited to him” were written not for him alone, but also for us, to whom God will credit righteousness—for us who believe in Him who raised Jesus our Lord from the dead. He was delivered over to death for our sins and was raised to life for our justification. (Romans 4:22-25)

There are no works or actions we can do but merely accept and believe God did what He did for us. The results and implications of this will be looked at in Romans Chapter 5.