The last-minute conversion to Jesus Christ in the Bible is the case of the criminal crucified alongside Jesus.
Luke 23:39-43 NKJV
Then one of the criminals who were hanged blasphemed Him, saying, “If You are the Christ, save Yourself and us.”  But the other, answering, rebuked him, saying, “Do you not even fear God, seeing you are under the same condemnation?  And we indeed justly, for we receive the due reward of our deeds; but this Man has done nothing wrong.”  Then he said to Jesus, “Lord, remember me when You come into Your kingdom.”  And Jesus said to him, “Assuredly, I say to you, today you will be with Me in Paradise.”
Only moments before his own death, this criminal had been an unbelieving mocker of Jesus Christ.
Matthew 27:44 NKJV
Even the robbers who were crucified with Him reviled Him with the same thing.
However, at the last moment the criminal repented and acknowledged Jesus as the Heavenly King. The Lord gave him the blessed promise, “Today you shall be with Me in Paradise.”
Although the story of the criminal on the cross demonstrates that last-minute conversions are possible, the Bible warns us to repent now, without waiting another moment. John the Baptist warned, “Repent, for the kingdom of heaven is at hand” (Matthew 3:2).
Jesus had the identical message concerning the need for immediate repentance, “Repent, for the kingdom of heaven is at hand” (Matthew 4:17).
The Bible warns us concerning the brevity of the human lifespan.
“You are just a vapor that appears for a little while and then vanishes away” (James 4:14).
We are not instructed to consider converting someday, but to believe today!
“Today if you hear his voice, do not harden your hearts”
Hebrews 3:7-15 NASB
Therefore, just as the Holy Spirit says, “Today IF YOU HEAR HIS VOICE,  Do NOT HARDEN YOUR HEARTS AS WHEN THEY PROVOKED ME, AS IN THE DAY OF TRIAL IN THE WILDERNESS,  Where YOUR FATHERS TRIED Me BY TESTING Me, AND SAW MY WORKS FOR forty YEARS.  “Therefore I WAS ANGRY WITH THIS GENERATION, AND SAID, ‘THEY ALWAYS GO ASTRAY IN THEIR HEART, AND THEY DID NOT KNOW MY WAYS’;  As I SWORE IN MY WRATH, ‘THEY SHALL NOT ENTER MY REST.'”  Take care, brethren, that there not be in any one of you an evil, unbelieving heart that falls away from the living God.  But encourage one another day after day, as long as it is still called “Today,” so that none of you will be hardened by the deceitfulness of sin.  For we have become partakers of Christ, if we hold fast the beginning of our assurance firm until the end,  while it is said, “Today IF YOU HEAR HIS VOICE, DO NOT HARDEN YOUR HEARTS, AS WHEN THEY PROVOKED ME.”
Hebrews 4:7 NASB
He again fixes a certain day, “Today,” saying through David after so long a time just as has been said before, “Today IF YOU HEAR HIS VOICE, DO NOT HARDEN YOUR HEARTS.”
None of us knows how much time we have left in this life or what the circumstances of our death will be. We may die in a sudden, unexpected manner that will preclude a deathbed conversion. The only reasonable option is to repent and believe in Jesus Christ today.
Many people die without having the experience of an extended amount of time on a death bed. Many people die instantly and unexpectedly, with no opportunity to trust in Christ.
“That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.”
2 Corinthians 6:2
“In the time of my favor I heard you, and in the day of salvation I helped you. I tell you, now is the time of God’s favor, now is the day of salvation.”