But that confuses repentance with conviction. Repentance is the fruit of faith, not its cause. You cannot truly hate sin, not in the genuine sense, unless you love God and you cannot love God without faith in Christ. What is more, since you haven't the strength to turn from sin to righteousness yourself, you can only do that through the power of Christ and that power is given only to those who believe in Jesus and turn to him for grace to help in time of need. Our fathers in the Reformed church made a great deal of this point.
Faith is the essential prerequisite of true repentance.
Years ago there was a Hindu society in India that sought to take everything positive in Christianity without compromising its Hinduism. They took over the Westminster Shorter Catechism definition of repentance, leaving out just two words. Repentance unto life is a saving grace whereby a sinner, out of a true sense of his sin and apprehension of the mercy of God in Christ, doth, with grief and hatred of his sin, turn from it unto God with full purpose of and endeavor after new obedience. But Paul would say, there is no repentance and can be none that is not in Christ. Without Christ and faith in him one cannot really turn to God or turn away from sin.