Post Alexander, the region was fought over & bounced between the Seleucid’s and Assyrian dynasties. Judea / Samaria became almost a buffer zone between these 2 superpowers. As their (Seleucid & Assyrian’s) power waned the Roman Empire stepped in to administer the region.
The Jews were always a difficult people to rule - they were an anomaly in the region, being monotheists, dietary laws etc…. The Roman’s gave greater religious freedoms to the Jews than they previously had under previous rulers.
This is usually referred to as the inter testamental period - stretch it from 200 bce to 100 ace for this conversation. & during this period we have Hellenism - the take up of the Greco-Roman religion/law/phillosopy. The age old problem of modernism within a religious community.
Jews did not want to be assimilated and ruled by Hellenism. There were plenty of revolutionary Jews ie Maccabean revolt which ended in about 160 bce in Masada. A last hilltop stand against the Romans.
Under Pompey in 60 bce and Titus in 70 ce Roman soldiers entered the Jerusalem Temple. Pompey entered the Holy of Holiest itself and defied the Temple. Titus caused the first Temple to be destroyed and the Jewish War. Gentiles entering the inner Temple. Wearing insignias of Caesar - a self declared living god was a defilement.
So although nothing was written about Jesus per se - there are early writings by Tacitus (& others) about early Christians. So going back to the reference of King of the Jews - an insult by the Romans to both Jesus and the Jews. They (Jews) would never refer to a Jewish leader as ‘King’ - that would be a title given to G_d. Nagid not malek - prince not king.
The Romans would have seen Jesus as a splinter group of Judaism like the Essenes.
An interesting period in time.