They are brought to life----regeneration---so they are able and willing to believe---have faith. They are saved by an act of grace (no one deserves it and can do nothing to merity it) through faith. It is this faith (in the person and work of Jesus) that justifies---reconciles them to God. The substitutionary work of Jesus is applied to them, (by the Holy Spirit, not by baptism) therefore their sins are forgiven. And the faith is not generated from within themselves, thereby meriting the new birth and meriting forgiveness, (making grace no longer grace but reward for a job well done). God is causal of all of it including faith.
When you say
you have contradicted yourself. If baptism is not causal, then it cannot be
If that is the case, then baptism is causal of regeneration, not God. It cannot be both symbolic and the cause of regeneration. If it is all of God, and only he is causal, then the regeneration must come before everything else. And everything else other than the baptism must also be caused by God or we have things not caused by God, though you say only God is causal. Baptism is a sign of being in the new covenant community---a visible confession of faith and union with Christ.
God and only God can cause anyone to be saved. There is no other cause. Salvation is a promise that God has made to humanity that He will act upon with and for those who have met with the conditions laid down for it. Those conditions are succinctly presented in Mark 16:16. Baptism is not causal. Not even faith is causal. They are conditions. Believing, having faith, in God and being baptized are two of those conditions. Regeneration is simply one aspect of God's saving actions.
And backing up a bit in your post, faith is indeed generated from within ourselves. Believing in God is not really that different from believing in anything else. One first believes the information and data available is true. Then from that, one places his trust and confidence in what he believes is true. That is the message of Romans 10.
I believe in gravity, not just something that pulls me toward the earth. I believe in gravity to be a controlling factor in the interactions between bodies of mass throughout the entire universe. I have no way to prove that. First I know that things tend to be apparently pulled toward the earth. There is actual data, from moon landings, to show that it works on the moon just like it does here on the earth. There is massive amounts of data and information to show that it works the same for the planets in this solar system as well as in other parts of the Milky Way and the rest of the universe. I am convinced in the truth of gravity. I trust that it will function as described. I believe in gravity. I have faith in gravity.
In much the same way, given the information and data supplied in the Bible, I believe that it is true. Not only do I believe it is true, I have placed my trust in God, the author of what is presented there. I have no other basis or reason for doing that.
Faith is not some sort of injected instinct as so many seem to think. One does not have faith and then hear the word of God. One hears (and/or reads) the word of God and by that believes and trusts that. That is faith. For some, like many and many that I know, it was not difficult to have faith, being raised in a good God-fearing Christian family. For others, that I also know, it can be difficult if not very, very difficult to come to believing in God. For some it takes hard work and many hours reading, studying and talking with others to finally come to faith.