Does Christ require the sinner to "stop sinning and you'll be pardoned"?, or something else?
When you trust in Christ for the first time, you are trusting in Him as a Savior FROM SIN, both its guilt and power. No one "just believes" in Christ's existence to be saved; we come to him, rather, to be rescued from sin's tyranny. We know we can do nothing to save ourselves from sin so we (by the grace of God) turn to Christ to be rescued from it. This demonstrates, without a doubt, that at the time you trust Christ you no longer want to be under sin's tyranny or dominion but want Christ to deliver you from it.
So in our initial repentance we are not called to "stop sinning and you'll be pardoned." No, rather its "Lord. I am a slave to sin, save me and break the chains of my sin and forgive. I have no hope without you" Thus, to want to be saved by Christ from sin already reveals a heart of repentance in it. Otherwise you would not want to be saved at all.
If you see faith as merely a belief in God's existence then YES faith precedes repentance, but if you define faith as trusting in Christ as Savior from sin, then while faith and repentance can be distinguished, they cannot be separated.
Consider: For what purpose are you coming to faith in Jesus if not to be rescued from sin?
NOTE: Christ intended to pardon us prior to both our faith and repentance, so neither faith nor repentance are actually the originating cause of our pardon. Pardon was purchased in Christ's redemption for us. The application of our redemption is when the Holy Spirit brings us into union with Christ's death and resurrection. He regenerates us, our faith and repentance springs from our renewed heart which issues from God's grace alone.