A grave error is that Old Testament (pre-incarnation of Christ) saints were saved because of their obedience to the law.
The reality is that all the saved -- Adam, Eve, Abraham, Isaac, Sarah, and us -- are saved by trusting in the mercies of God.
A couple of weeks back, I suggested that the book of Esther is a book about evangelism, about how "many of the people of the land became Jews; for the fear of the Jews fell upon them." (8.17b)
We sometimes imagine that the Old Testament people of God was a physical thing. In one sense it was. But in the most important sense, the people of God are God's people because of that trust in God's mercies. (Cf. Romans 9.6: "they are not all Israel, which are of Israel").
A verse which helps to make Romans 9 plainer is Psalm 73.1: "Truly God is good to Israel, even to such as are of a clean heart."
The verse is a parallelism. "God is good to Israel," and Israel is defined as those with a clean heart. Not physical lineage -- as blessed as that is, especially delineated in Romans 3 -- but those -- whether born Jew or Gentile who have a clean heart.
And how do we get a clean heart? By working hard? By our own efforts? The answer's in Psalm 51.10: "Create in me a clean heart, O God; and renew a right spirit within me."
God creates us in the first place, and then He creates a clean heart in us. God makes us "the Israel of God" (cf. Gal. 6.16) by creating a clean heart in us, and by removing our "heart of stone." (Ezekiel 36.26)