Faith's importance to salvation is accentuated by this verse. Faith plays a role in the entire process until we enter the Kingdom of God. It is the sum of what God is doing in our lives: "Jesus answered and said to them, 'This is the work of God, that you believe in Him whom He sent'" (John 6:29). In the fourth and fifth chapters of Romans, Paul mentions faith a dozen times, almost all concerning justification, being made righteous or having access to grace, and thus, having the hope of the glory of God.
The faith that saves has its beginning when God, on His own initiative, calls us (John 6:44) and leads us to repentance (Romans 2:4). He does this by His Spirit guiding us into all truth (John 16:7-14). Stirring up our minds to knowledge, His Spirit enables us to perceive from a perspective we never before seriously considered. This, combined with the confrontation that occurs with the carnal mind when we are forced to choose what to do with this precious truth, gives birth to a living faith, a faith that works, a faith that walks in godliness.
This would never occur if God did not first do His part. We would never find the true God on our own or understand His gospel of the Kingdom of God. We would never be able to choose the real Jesus, our Savior and Elder Brother, from the mass of false christs created in the minds of men. Not knowing what to repent of or toward, we would never repent.
As miraculous and powerful as God's liberation of Israel from bondage was, even more so and of greater importance is the breaking of our bondage to Satan, this world, and human nature. This is why Ephesians 2:8 says the faith that saves is "the gift of God." Israel's release from Egypt was God's gift too. Regardless of how much they cried out to Him, the Israelites would never have left Egypt without Him. If God had not been merciful and faithful, if He had not been trustworthy, they would never have been freed.