I know the Bible speaks of the Judgment Seat, which is not about judgment re: salvation (which is based on faith) but about one's works on earth that may be rewarded in Heaven. This seems to be directed entirely toward those who already believe. Revelations speaks of the second judgment, and it is directed toward unbelievers. But is it specified that "belief" must occur during mortal life? Do we know from the Bible that earthly nonbelievers are not given a chance to accept/reject Christ after death?
Romans 14:10 - 12
ESV - 10 Why do you pass judgment on your brother? Or you, why do you despise your brother? For we will all stand before the judgment seat of God. 11 For it is written, "As I live, says the Lord, every knee shall bow to me, and every tongue shall confess to God.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.