“What shall we say, then? That Gentiles who did not pursue righteousness have attained it, that is, a righteousness that is by faith; but that Israel who pursued a law that would lead to righteousnessdid not succeed in reaching that law. Why? Because they did not pursue it by faith, but as if it were based on works. They have stumbled over the stumbling stone, as it is written, “Behold, I am laying in Zion a stone of stumbling, and a rock of offense; and whoever believes in him will not be put to shame.”
Brothers, my heart’s desire and prayer to God for them is that they may be saved. For I bear them witness that they have a zeal for God, but not according to knowledge. For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God’s righteousness. For Christ is the end of the law for righteousness to everyone who believes.
For Moses writes about the righteousness that is based on the law, that the person who does the commandments shall live by them. But the righteousness based on faith says, “Do not say in your heart, ‘Who will ascend into heaven?’” (that is, to bring Christ down) “or ‘Who will descend into the abyss?’” (that is, to bring Christ up from the dead). But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith that we proclaim); because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. For the Scripture says, “Everyone who believes in him will not be put to shame.” For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him. For “everyone who calls on the name of the Lord will be saved.”
How then will they call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching? And how are they to preach unless they are sent? As it is written, “How beautiful are the feet of those who preach the good news!” But they have not all obeyed the gospel. For Isaiah says, “Lord, who has believed what he has heard from us?” So faith comes from hearing, and hearing through the word of Christ.
But I ask, have they not heard? Indeed they have, for “Their voice has gone out to all the earth, and their words to the ends of the world.”
But I ask, did Israel not understand? First Moses says, “I will make you jealous of those who are not a nation; with a foolish nation I will make you angry.”
Then Isaiah is so bold as to say, “I have been found by those who did not seek me; I have shown myself to those who did not ask for me.”
But of Israel he says, “All day long I have held out my hands to a disobedient and contrary people.”” (Romans 9:30–10:21 ESV)

The Jews were not justified before God in their ardent attempts at keeping the Law.  They did not attain acceptance before God because they pursued it based on their own efforts instead of by faith; they, much like us, thought that they could perform well enough to earn God’s approval and blessing (9:30-32).  They were ignorant of the how to be righteous before God and worked tirelessly to establish their own righteousness.  But this was to no avail (and still is) because Christ has become our righteousness as a result of His perfect law keeping, and this is given to us by faith.
Paul exposes works based righteousness by quoting Moses in Leviticus 10:5 and says “that the person who does the commandments shall live by them” (Romans 10:5).  This is very attractive to our flesh, we like to point to this and say that if we try really hard we can merit God’s affection and favor.  The problem with this line of thinking is that Paul spends the first three chapters of this very letter unpacking that no one can keep the law perfectly, except Jesus.  The many passages in the Old Testament that tell us that righteousness comes from obedience to the Law are properly interpreted by seeing Christ as the perfect law keeper on our behalf, therefore making us righteous (10:6-8).  God’s requirement is not our perfect adherence to His perfect Law, God’s requirement is faith in the Perfect Law Keeper that attained right standing for us.  Belief in Christ, not our own works based righteousness is how we are justified before God (Romans 10:11).   The Gentiles who did not seek after God (like the Jews) are the ones that found Him – according to His sovereign plans for His glory (10:20).