I am sorry, I was operating under the assumption that our frame of reference was from the Fall until the Second Coming. Clearly, Adam and Eve fell because of their lack obedience. But before they fell the did not need saving either. So you have a moot point I think. Therefore, even after the Fall, Adam and Eve were saved by faith alone no personal works included.

Besides our faith in God does not save us. Even the devils believe in God and they tremble. We are saved because we place our faith and trust in Christ to save us. This is more than just a mere belief in God, but rather a specific trusting in God's Son, Jesus Christ, and the substitutionary atonement He made for us on the cross.