The answer is found in the New Testament word "wash."
Spiritual washing is one part of the three-fold action performed by God upon a person at the point of faith. All at one moment God washes our hearts, sets us apart for Himself, and justifies us of our sins (1 Corinthians 6:11). This spiritual washing experience causes a person to become holy -- not just "positionally", but actually (Ephesians 5:26). Spiritual washing cleanses our souls/consciences of the guilt of our sins (Hebrews 10:22).
The Bible is clear that faith in Christ is the condition that must be met for anyone to be justified (Romans 3:24-25). We are also sanctified on the condition of faith in Christ (Acts 26:18). Faith in Christ is the sole condition for forgiveness of sin (Acts 10:43).
Regeneration means "to spiritually wash" (Titus 3:5). So, based on that meaning, we see that we are regenerated on the condition of faith in Christ. The Biblical order is faith first, resulting in the new birth.
John Calvin's error -- this Reformation tradition of calling the Lord's pre-faith work "regeneration" -- has been a source of confusion to believers for centuries. Calvin was right to teach that the Lord must work in the heart, for anyone to trust in Christ. His error lay in naming that work "the new birth". Jesus, in John 6, instead called this work "drawing."
The lesson for us here is that we should use inductive Bible study methods to define Bible words, comparing verse to verse. Do not follow doctrinal creeds or traditions when it can be shown that they have erred.