God has designed mankind with certain capacities and abilities which have been retained despite the Fall, even though everything about us has been tainted from being born apart from God and controlled by self-will. We have a capacity to believe, even as sinners, though left to our own devices that capacity ignores God as he is and opts for gods of our own construction. I would call this circumstance, Latency. There is a capacity for faith built into the human being by God and it exists, even if imperfect and impotent, within every human being.
Left to our own devices, we would never bother with the true God. The ones we make up are much more manageable and a lot less scary. Some opt for the most dismal and foolish alternative in not bothering with gods at all. We would wander off to hell obliviously if something or someone didn't disrupt our journey. Without a catalyst acting upon our latent capacity for true faith in the true God, we would never cross the threshold of believing unto righteousness. What was not possible in ourselves becomes possible with the intervention of God. Let's call this disruption, Interference. This gracious interposition comes our way by the word of Christ and the conviction of the Holy Spirit.
If something did not conserve the impact of God's interference, which gave faith an opportunity to sprout, we would quickly devolve back to our former state, or worse, soon after experiencing it. We need a restructuring of our mind/body/spirit combo if we are to experience any lasting effect from God's interference. When faith is expressed in Christ due to the influence of God's interference, God reinspires the dead human spirit causing one to be born again. Let me call that infusion, Regeneration. Without that renewal, no human being is either fit or able to enter into God's kingdom.
From start to finish, the remaking of a lost sinner into a child of God is God's doing. Latency and interference giving rise to regeneration was his idea, and proceeds according to his design. That it is conditioned on faith in the sinner changes nothing, it is as God wants it to be.