To Whom Did Jesus Appear? - 1 Corinthians 15:5-8

1 Corinthians 15:5-8 [A]nd that [Christ] appeared to Cephas, then to the twelve. Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. Then he appeared to James, then to all the apostles. Last of all, as to one untimely born, he appeared also to me.

Jesus did appear before unbelievers. Initially even Jesus' own disciples had temporarily abandoned him - abandoning even the resurrection (Luke 24:11, 25 - see Jesus and the Table). Thomas doubted (John 20:25). In 1 Corinthians 5:7 Jesus appeared before his own unbelieving brother James, not James the brother of John and one of the Twelve. James, the Lord's brother, only believed AFTER the resurrection - John 7:5; Gal. 1:19). Also, Jesus then appeared before the unbelieving Saul of Tarsus, later known as Paul (Acts 9). The resurrection is an unmistakable historical fact as attested to by both believers and unbelievers.

Please also see:

The Resurrection of Christ:
A Historical Fact, by B. B. Warfiled.

The Resurrection of Christ, by John Calvin.

The Resurrection of Christ, by Augustus Montague Toplady.