The most fascinating thing about Romans 10 is that it follows Romans 9! God elects/chooses for his purposes. . . AND whoever calls on the name of the Lord will be saved. As Paul prays for the salvation of his countrymen, he details the free offer of salvation, all in the context of God's electing/choosing grace! Oh, that we would see the connection and get both!
The problem is that they have a zeal for God that is ignorant. They want something else, not the real deal. They are unsubmissieve because they don't know the righteousness of God and create a substitute. And. . . there is no substitute. Christ is righteousness.
The Old Testament Scriptures saturate this chapter and form the foundation of the offer of salvation. This is not new that salvation comes through faith. Don't think for a moment that Old Testament believers were saved another way. It is not new, either, that God will give salvation to the Gentiles.