You are talking out of both sides of your mouth. When someone is walking in the flesh, they are sinning because they are living independently of God. And if they aren't indwelt by the Spirit of God, they can only walk according to the flesh. Further, no one operating in the flesh is exercising faith. They aren't pleasing God.Not necessarily.
But walking in and after the "flesh" kept them away from God.
OT men, in general, could exercise faith.
Abraham and Noah, for example.
Also, Simeon and Anna, at the temple when the newborn Jesus was presented by His parents. (Luke 2:25-38)
However, until rebirth was made possible, they were all sons and daughters of Adam and Eve...not of God.
OT saints were saved the same way everyone is saved: by grace through faith. And they, like NT saints, could do nothing apart from Christ.