Why would a JEW who rejected Christ give credit to Christ. The Jews wanted to ignore Christ and his power. Much like how our news media tends to ignore news that they don't think fits their narrative today. A great example just admitted Hunter's laptop is genuine after over 750 days of ignoring it. A Jew wouldn't recognize things that threatened his personal power as a Jew. Christ's message threatened to dissolve Jewish religion.
The first century Jewish historian Josephus wrote about Jesus and his execution by Roman authorities.
There was no reason for Jesus to be widely known before the late first century. He was an obscure Jewish mystic who mainly taught in the backwater province of Galilee to a relatively small following of Jewish peasants. The New Testament obviously embellishes and idealizes his actions and importance prior to 30 CE. To the Romans, Jesus was just one of dozens of Jewish mystics preaching an apocalyptic message.
History was not written down in antiquity in the format we are accustomed to today. That said, the histories part of the Old Testament is about as good a historical source as we can get, and it is substantially superior to any histories left to us by the Mesopotamians, Hittites, or Assyrians.
Acts in the new testament is generally considered of significant value to historians for it's historical information (though sometimes idealized) on the early Christian communities.