Gal 3:11 The just shall live by his faith

Gal 3:11
But that no one is justified by the law in the sight of God is evident, for “the just shall live by faith.”
Yet the law is not of faith, but “the man who does them shall live by them.”[fn].
Hab 2:4
Behold, his soul which is lifted up is not upright in him: but the just shall live by his faith.
So this is not a New Testament concept.
Lev 18:5 Ye shall therefore keep my statutes, and my judgments: which if a man do, he shall live in them: I am the LORD.
A very good discussion of both of these verses quoted by Paul in Gal.
Hab 2:4 is seen as a Messaianic text in the Talmid that is faith in the coming Messiah will bring salvation. And Had 2:4 was used to summarize all 613 laws. Paul had to have known this since it is the Jewish sages who he studied.