How about the story of the prodigal son? He was dead according to the father, yet lived. We read that the prodigal came to himself and went back to the father. We read nothing that says the father caused him to be alive again, and then he returned.The sinner is apart from the life of God, dead in trespasses and sins, is ignorant, is without understanding, is blind to spiritual truth, doubly blinded by Satan and the world as well, and in that condition there is nothing he can do for himself to become alive.
You think by some prayer, by way of an altar call, you can woo your way to Life. You might as well try to raise somebody at the local mortuary, or even better yet, go to the nearest graveyard and try pleading with the corpses to see if they can raise themselves from the dead. It can't be done. Life has to come from the one who is the source of life, God Himself. And if there's going to be any response, then there has to be a work of God prior to that response. And that is what the Bible calls regeneration.
You're talking to several here from the Church of Christ. Your point about prayers and altar calls falls flat with most of this group because we believe those to be damnable lies.
You are not going to get any takers on the idea that man must be reborn even before faith. We all believe, in one form or another, that faith is the cause of mans' new birth.