Josephus Flavius, the Jewish historian, lived as the earliest non-Christian who mentions a Jesus. Although many scholars think that Josephus' short accounts of Jesus (in Antiquities) came from interpolations perpetrated by a later Church father (most likely, Eusebius), Josephus' birth in 37 C.E., well after the alleged crucifixion of Jesus, puts him out of range of an eyewitness account. Moreover, he wrote Antiquities in 93 C.E., after the first gospels got written! Therefore, even if his accounts about Jesus came from his hand, his information could only serve as hearsay.
Pliny the Younger, a Roman official, got born in 62 C.E. His letter about the Christians only shows that he got his information from Christian believers themselves. Regardless, his birth date puts him out of the range of eyewitness accounts.
Tacitus, the Roman historian's birth year at 64 C.E., puts him well after the alleged life of Jesus. He gives a brief mention of a "Christus" in his Annals (Book XV, Sec. 44), which he wrote around 109 C.E. He gives no source for his material. Although many have disputed the authenticity of Tacitus' mention of Jesus, the very fact that his birth happened after the alleged Jesus and wrote the Annals during the formation of Christianity, shows that his writing can only provide us with hearsay accounts.
Suetonius, a Roman historian, born in 69 C.E. mentions a "Chrestus," a common name. Apologists assume that "Chrestus" means "Christ" (a disputable claim). But even if Seutonius had meant "Christ," it still says nothing about an earthly Jesus. Just like all the others, Suetonius' birth occurred well after the purported Jesus. Again, only hearsay.
Talmud: Amazingly some Christians use brief portions of the Talmud, (a collection of Jewish civil a religious law, including commentaries on the Torah), as evidence for Jesus. They claim that Yeshu (a common name in Jewish literature) in the Talmud refers to Jesus. However, this Jesus, according to Gerald Massey actually depicts a disciple of Jehoshua Ben-Perachia at least a century before the alleged Christian Jesus. [Massey] Regardless of how one interprets this, the Palestinian Talmud got written between the 3rd and 5th century C.E., and the Babylonian Talmud between the 3rd and 6th century C.E., at least two centuries after the alleged crucifixion! At best it can only serve as a controversial Christian and pagan legend; it cannot possibly serve as evidence for a historical Jesus.