Not so-
Your statement "Christ did not die for the sin of unbelief" is incorrect from a Christian theological perspective.
The Bible clearly teaches that Christ died for the sins of all humankind, including the sin of unbelief.
Firstly, the Bible makes it abundantly clear that Christ died for the sins of all people. 1 John 2:2 (ESV) states, "He is the propitiation for our sins, and not only for ours but also for the sins of the whole world."
Similarly, Titus 2:14 (ESV) proclaims, "who gave himself for us to redeem us from all lawlessness and to purify for himself a people for his own possession who are zealous for good works."
These verses indicate that Christ's death extends to cover the sins of everyone, including the sin of unbelief.
Secondly, the Bible teaches that unbelief itself is a form of sin. Hebrews 3:12 (ESV) warns against hardening one's heart toward God, stating, "Take care, brothers, lest there be in any of you an evil, unbelieving heart, leading you to fall away from the living God." Furthermore, Mark 16:16 (ESV) notes that those who do not believe in Christ will face judgment, indicating that unbelief is a sin deserving punishment.
Thirdly, the Bible reveals that Christ's death covers every kind of sin, even those committed unwillingly or ignorantly. Matthew 12:31-32 (ESV) states, "Therefore I tell you, every sin and blasphemy will be forgiven people, but the blasphemy against the Spirit will not be forgiven. And whoever speaks a word against the Son of Man will be forgiven, but whoever speaks against the Holy Spirit will not be forgiven, either in this age or in the age to come." This passage shows that Christ's death covers all kinds of sins except for the deliberate rejection of the Holy Spirit.