Yes, the expression of one's sincere sorrow for a life lived in sin is essential as an element of salvation along with faith in Jesus as Messiah but I say this with an often times misunderstood caveat.

One expresses their sorrow for a sinful life and a sincere desire to repent at Salvation but true repentance is not possible until the Holy Spirit takes up residence within the believer as Guarantor of New Covenant relationship (Ephesians 1:13-14) and the believer begins their daily walk in Christian sanctification where the Spirit combines the "new creation" in Jesus (2 Corinthians 5:17) with the enlivened spiritual law written upon the heart (Hebrews 10:16); it is at this juncture that obedience/repentance is realized through the production of divine fruit (Galatians 5:22-23) in the daily life of those who belong to Jesus by faith (Galatians 5:16-23; John 15:8).

Yes, Jesus has told us that unless one repents they will in no way enter the Kingdom of Elohim (Luke 13:3) and sincere sorrow for a life of sin expressed as part of the salvation confession is essential in combination with sincere faith-belief that Jesus is Messiah but the realization of true repentance, actuated repentance, does NOT manifest until subsequent salvation as this true repentance is only possible by obedience to the indwelling Holy Spirit who is Guarantor of New Covenant relationship with the Father established by faith in Jesus as Messiah (Ephesians 1:13-14).

It is not necessary nor is it possible that one "change their life" first in order to receive the promise of salvation by faith but it is necessary that one express true sorrow for a life lived in disobedience while simultaneously possessing a heart that desires divine "change" in combination with faith, faith that Jesus is Messiah who died for our sin and it is the Holy Spirit who takes the sincere desire for "change" and makes that change a reality through His divine work in daily sanctification via the production of divine fruit; Jesus said, "You will know them by their fruit" (Matthew 7:15-20).

Therefore, you cannot sufficiently clean-purify yourself by good works in order to make yourself righteous before Elohim (Galatians 2:16; Romans 3:21), only the Holy Spirit changes the human heart and the Spirit only works sanctification in the life of the one who expresses sincere faith in Jesus as Messiah. You are "made righteous" through the "imputation" or gifting of Messiah's righteousness over your life by faith in Him as your Messiah (2 Corinthians 5:21); this, by faith in Jesus, and you are only sanctified through the work of the indwelling Holy Spirit during daily sanctification, a life-long process where the Holy Spirit prepares the redeemed in Jesus for service in the New Jerusalem (Galatians 5:16); it is during daily sanctification that true repentance manifests through the production of divine fruit (John 15:8; Matthew 3:8).

If you offended me and hated me and ridiculed me through your actions and words but came to me asking for a favor or intercession due my unique ability to provide that "favor" but you remained in your offensive posture...why would I entertain your request seeing that you express no desire to change your attitude toward me? Why would Elohim entertain the prayer for salvation offered by one who had no intent or desire to change their obsession with the Adamic sin-nature?