A key passage on this topic is in Romans, Chapters 3-5. It is part of a long argument, in which the Apostle Paul is discussing the doctrine of Justification - how people can be made right with God. We can’t look at the whole passage in this answer, but we suggest you read it through for yourself. The heart of the answer to this question is found in Romans 4:9-11:  “... We have been saying that Abraham’s faith was credited to him as righteousness. 10 Under what circumstances was it credited? Was it after he was circumcised, or before? It was not after, but before! 11 And he received circumcision as a sign, a seal of the righteousness that he had by faith while he was still uncircumcised.”

Paul’s argument hinges on Abraham. Abraham is a man who is held up in the Old Testament as God’s chosen man, a man who is declared righteous by God in Genesis 15:6: “Abram believed the Lord, and he credited it to him as righteousness.” In the verses in Romans, Paul is showing that Abraham was declared righteous by God because of his faith, and it can’t have been anything to do with the law or good works (of which Paul uses circumcision as an example), because the law hadn’t yet been given. Abraham was declared righteous by God because of his faith, which was expressed in his obedience to the Lord by getting circumcised (among other things). Paul is saying that faith is always the way that God’s people have been justified,  both before Christ’s death and resurrection and after Christ’s death and resurrection. He goes on to make this connection explicit in Romans 4:23-25: “23 The words ‘it was credited to him’ were written not for him alone, 24 but also for us, to whom God will credit righteousness – for us who believe in him who raised Jesus our Lord from the dead. 25 He was delivered over to death for our sins and was raised to life for our justification.”

Paul is clear that this faith itself is not a ‘work’ by which we earn our salvation, but is a gift, given to us by His grace. Neither Jews nor Gentiles have done anything to justify themselves, God justifies them by His grace alone, through faith in Him. Paul mentions the grace of God in this regard in Romans 3:22-24: “22 This righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, 23 for all have sinned and fall short of the glory of God, 24 and all are justified freely by his grace through the redemption that came by Christ Jesus” and again in Romans 5:1-2: “Therefore, since we have been justified through faith, we have peace with God through our Lord Jesus Christ, 2 through whom we have gained access by faith into this grace in which we now stand. And we boast in the hope of the glory of God.”

In summary, God has always saved his people and justified them in His sight because of faith in Him, not because of any good works they might have done. This is an act of his grace to us, as underserving people who have consistently fallen short of his standards.