You are mixing something important, and it changes the meaning of the truth.Why would anyone desire to cease from sinning before they believe in the gospel? Sin can only be understood relative to what the gospel teaches, so if someone doesn't believe the gospel, then neither would they care about sin. The same with dead works and repentance.
Repentance is a gift only given by God to someone from their salvation: it is only given to those whom He saves
[Rom 2:4 KJV] 4 Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance?
[2Ti 2:25 KJV] 25 In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth;
[Act 11:18 KJV] 18 When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
[Heb 9:14 KJV] 14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
If someone truly believes it is only because it was given to them by God as a result of their salvation. Since He does not do so to everyone, we can know that those that truly believe, are those He saved
[Jhn 6:29 KJV] 29 Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.
[Phl 1:29 KJV] 29 For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
[2Pe 1:1 KJV] 1 Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ:
You say people would not want to stop sinning unless they already believe. But Jesus shows the opposite. He calls people to turn from sin first, and then follow Him.
Jesus began His message like this:
“Repent: for the kingdom of heaven is at hand.” (Matthew 4:17, KJV)
He did not say, “You are already saved, so now repent.”
He called people to repent so they could enter the kingdom.
Look at how He spoke to sinners:
“I came not to call the righteous, but sinners to repentance.” (Luke 5:32, KJV)
They were still sinners. They were not saved yet. Yet He called them to repent.
And when He spoke to the woman caught in sin, He said:
“Go, and sin no more.” (John 8:11, KJV)
He did not tell her, “You will only stop sinning after salvation is given.”
He commanded her to turn away from sin.
Also, Jesus shows that people already know sin, even before fully understanding the gospel. Why? Because God’s law is already known in the heart, and Jesus points back to it:
“If thou wilt enter into life, keep the commandments.” (Matthew 19:17, KJV)
So sin is not first learned from the gospel. It is already known, and Jesus calls people to leave it.
Now about repentance being only for those already saved. Jesus again speaks clearly:
“Except ye repent, ye shall all likewise perish.” (Luke 13:3, KJV)
Repentance is not something after salvation. It is required so that you do not perish.
And again:
“They that are whole need not a physician; but they that are sick.” (Matthew 9:12, KJV)
A sick person must come to the doctor to be healed.
They are not healed first, and then come.
In the same way, a sinner turns (repents), comes to Christ, and then receives life.
You also said belief only comes after someone is already saved. But Jesus shows belief is the condition:
“He that believeth on him is not condemned: but he that believeth not is condemned already.” (John 3:18, KJV)
If someone is already saved before believing, how can unbelief still leave them condemned?
And again:
“If ye believe not that I am he, ye shall die in your sins.” (John 8:24, KJV)
So belief is not the result of salvation. It is required to escape death in sin.
Then Jesus joins belief and obedience together:
“And why call ye me, Lord, Lord, and do not the things which I say?” (Luke 6:46, KJV)
True faith is not something given after everything is finished. It is shown by turning, believing, and following.
People already know sin.
Jesus calls them to repent.
If they refuse, they perish.
If they repent and believe, they receive life.
God does lead people, yes. His goodness calls them. But Jesus never taught that a person is saved first and only then able to repent or believe.
He taught the opposite:
Turn, believe, and follow — so that you may live.