It's a common misconception among Christians: Old Testament believers (Israel) were saved by works, but New Testament believers (Christians) are saved by grace.
Nope. Wrong. Incorrect. Not even close.
Salvation/deliverance/redemption has never been achieved by works or merit. Never ever.
Noah found favor with God before Scripture says any word about his good works. His obedience came in response to God's selection of him to build the ark, not before.
Abraham was a pagan whom God called to faith before any good works are documented. His obedience came in response to God's work, not before.
Let's hold up just a minute...Let us not gloss over what Scripture says about these men and what it does not say about them. Let us not add anything to the story or speculate about how 'good' or 'righteous' either was before God called them lest we say something that God does not say and slip in even the slightest notion that they somehow merited or deserved their callings. I know that we want to find something in the story to 'prove' their worth, but not only will we not find it in Scripture but the whole idea goes against the idea of salvation by grace! Now back to the main point...
Israel was delivered/redeemed from Egyptian slavery before she was given the Law, not in response to keeping the Law. Summing things up through Moses before his death, God repeats all his acts of deliverance in Deuteronomy 10-11 then says 'therefore' Israel was called to walk in obedience.
Here are three examples from the opening pages of Scripture, but there are plenty more. I could go on and on and on and on and on...get it?
Obedience was never the cause for anyone's salvation or deliverance. Ever. That's one of the main points of the entire book of Galatians. In fact, Gal 2.16-21 goes even further, saying that if it was possible to be saved by good works, then Jesus died for nothing.
*Obedience is always only ever the response to God's prior grace. *
Paul's teaching in the NT, especially Galatians, makes it plan that the Jews of his day had corrupted God's gracious revelation. From the time of Moses to the time of the NT, what was given as a gracious covenantal relationship had become twisted into a religion of works righteousness and external obedience to the law as the means/basis/hope for salvation. Jesus' words in Matthew 5 also make this abundantly clear. "You have heard...but I say to you..."
Why on earth am I going out of my way to make this point? There are two reasons.
First, salvation under the Old Covenant happened exactly the same way as salvation in the New Covenant...by grace, through faith. The two looked very different, for sure, but salvation has always been by grace. Period.
Second, once we open the door to thinking that Noah, Abraham, or someone else was saved, called, or used by God because they deserved it, we open the door to thinking the same about us. This is the height of hubris and arrogance. "Did God really say...?" We all know how well that turned out.
Take heart. We don't deserve God's wonderful grace that he lavishes on us in Christ, but he does it anyway! That is the whole point. That is the best news ever.