Paul has presented the vital role faith plays in the life of every believer in the Lord Jesus Christ for salvation. Before moving on, he pauses to provide Biblical proof what he proposes is true.
The essence is this: “For what does the scripture say?”
(The reality is none of this is Paul’s idea or design but God’s.)
Given the only Bible they had in the days in which the Book of Romans was first written and read was the Old Testament, Paul goes there for two prominent examples justification is by faith alone.
There are no works of the Law which can overcome the condemnation of it.
Paul cites Abraham first as a great example, and as the (literal) father of our faith. Abraham believed what God said even though it was plainly impossible, and his belief in God, rather than his works for God established him as a righteous man.
Abraham believed God he would father a child in his old age – and father a nation, and he did. Without knowing, his faith in what God said fostered the lineage of Christ, who came from the lineage of David, who came from the lineage of Abraham.
And what of David, who deserved the worst of condemnation, but instead experienced the greatness of mercy and grace through his simple faith in the love of God?
In noting first Abraham and then David as faithful examples, Paul lays down the gauntlet for anyone to change this word of faith into some contrivance of the Law.
It must never happen.