My understanding is that the only "Christ, Son of God" references are found in the Bible and the ancient scripts it was based on. There are no city records of a Christ who ran around and shook up the Middle East 2000+ years ago.
But there is a record of a man named Christ:
The Roman historian and senator Tacitus referred to Christ, his execution by Pontius Pilate and the existence of early Christians in Rome in his final work.
The first-century Roman Tacitus,who is considered one of the more accurate historians of the ancient world,also mentioned superstitious “Christians” (from Christus,which is Latin for Christ),who suffered under Pontius Pilate during the reign of Tiberius. Suetonius,chief secretary to Emperor Hadrian,wrote that there was a man named Chrestus (or Christ) who lived during the first century.
Flavius Josephus is the most famous Jewish historian. In his Antiquities he refers to James,“the brother of Jesus,who was called Christ.” There is a controversial verse (18:3) that says,“Now there was about this time Jesus,a wise man,if it be lawful to call him a man. For he was one who wrought surprising feats....He was the Christ...he appeared to them alive again the third day,as the divine prophets had foretold these and ten thousand other wonderful things concerning him.” One version reads,“At this time there was a wise man named Jesus. His conduct was good and he was known to be virtuous. And many people from among the Jews and the other nations became his disciples. Pilate condemned him to be crucified and to die. But those who became his disciples did not abandon his discipleship. They reported that he had appeared to them three days after his crucifixion,and that he was alive; accordingly he was perhaps the Messiah,concerning whom the prophets have recounted wonders.