Those saved are made righteous through/because of Christ's faith, not theirs. Theirs comes FROM being born again. It does not make
them born again. Belief doesn't lead to eternal life, eternal life leads to belief. As cv5 posted:
[Act 13:48 KJV]
48 And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.