Will those who don't believe be forgiven of their sins?
Everyone is forgiven already on account of the death of Christ who suffered and died on behalf of all.
"While we were yet sinners, Christ died for us." (Romans 5:8)
"Christ Jesus came into the world to save sinners, and I am the chief of sinners." (1 Timothy 1:15)
"For God so loved the world that He gave His only-begotten Son, that whosoever should trust in Him should not perish but have eternal life." (John 3:16)
Do men have to make a confession of faith
The Scripture say,
"because if you confess with your lips that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For one believes with the heart and so is justified, and one confesses with the mouth and so is saved. The scripture says, “No one who believes in him will be put to shame.” For there is no distinction between Jew and Greek; the same Lord is Lord of all and is generous to all who call on him. For, 'Everyone who calls on the name of the Lord shall be saved.'" (Romans 10:9-13)
It is through faith that the Holy Spirit appropriates the work of Christ, as the Apostle says in the same chapter, "So faith comes from what is heard, and what is heard comes through the word of Christ." (Romans 10:17)
That by the preaching of the Gospel comes faith, and through faith God graciously justifies, imputing the righteousness of Christ freely, as a gift; this faith is God's gift and "not of ourselves" (Ephesians 2:8-9)
Romans 10 tells us that though we are not to judge who will ascend or who will descend, we do preach faith in CHRIST to all men which means men must hear and believe and confess JESUS with their mouth and in their heart
Some don't believe
And though HE died for the sins of men, some will die in their sins because they do not believe who HE says HE is
And that has nothing to do with the fact that Christ's work is insufficient or ineffectual; but everything to do with human volition being sinful, broken, and in opposition to God; as the Apostle, quoting the Psalmist writes, "There is none who seek God, no not one" (Romans 3:11) and the Prophet Jeremiah who has written, "The heart is deceitful above all things, and desperately sick, who can understand it?" (Jeremiah 17:9); it is therefore not up to man to do what is right in the sight of God in order to earn God's favor, it is instead God who has accomplished our salvation for us already, by sending His Son, our Lord Jesus, who suffered under Pontius Pilate, was crucified, buried, and dead, and who rose on the third day. He has thereby won for us salvation, forgiveness, eternal life, and victory over sin, death, hell, and the devil. He has accomplished this, for our good, in accordance with God's will, love, and kindness.
So yes, Christ died for the unbelieving, Christ died for all sinners, and by His death there is forgiveness of sin--of all sins, everyone's sins, without condition. Christ alone has done this, God has done it all. Glory to God alone.
-CryptoLutheran