I believe that saving Faith is more than just belief. I believe that saving Faith is actually TRUST in God.
Adam and Eve DIDN’T Trust God - they surely believed in God but they didn’t TRUST what God said about taking and eating of the forbidden fruit.
Therefore, are we saved by TRUST alone - yes. But not by belief alone. TRUST is an EVIDENT attribute to ones character.
So while Adam and Eve sinned by distrust, God has provided through the second Adam (Jesus) reconciliation through Trust. Since Trust is an EVIDENT attribute, and possessing that trust means the person will be in obedience to the Law of God. Not the letter of the law but to the Holy Spirit.