I think Paul could be the Saul mentioned in Josephus (who lived at least up to 66 CE). Saul was related to the Herodians, as is commonly argued for Paul (e.g, Rom. 16:11: "Greet my kinsman Herodion"), and both were pro-Roman:
War 2.17.4:
So the men of power perceiving that the sedition was too hard for them to subdue, and that the danger which would arise from the Romans would come upon them first of all, endeavored to save themselves, and sent ambassadors, some to Florus, the chief of which was Simon the son of Ananias; and others to Agrippa, among whom the most eminent were Saul, and Antipas, and Costobarus, who were of the king's kindred; and they desired of them both that they would come with an army to the city, and cut off the seditious before it should be too hard to be subdued.
Cf. Rom. 13:1-7:
Everyone must submit himself to the governing authorities, for there is no authority except that which is from God. The authorities that exist have been appointed by God. Consequently, the one who resists authority is opposing what God has set in place, and those who do so will bring judgment on themselves.
For rulers are not a terror to good conduct, but bad. Do you want to be unafraid of the one in authority? Then do what is right, and you will have his approval. For he is God’s servant for your good. But if you do wrong, be afraid, for he does not carry the sword in vain. He is God’s servant, an agent of retribution to the wrongdoer.
Therefore, it is necessary to submit to authority, not only to avoid punishment, but also as a matter of conscience. This is also why you pay taxes. For the authorities are God’s servants, who devote themselves to their work. Pay everyone what you owe him: taxes to whom taxes are due, revenue to whom revenue is due, respect to whom respect is due, honor to whom honor is due.
Both were acquainted with "those of Caesar's household" and were forced to flee from Jerusalem (if there is anything to 1 Thess. 2:14-16, and I think that there is anyway):
War 2.20.1:
After this calamity had befallen Cestius [in 66 CE], many of the most eminent of the Jews swam away from the city, as from a ship when it was going to sink; Costobarus, therefore, and Saul, who were brethren, together with Philip, the son of Jacimus, who was the commander of king Agrippa's forces, ran away from the city, and went to Cestius. But then how Antipas, who had been besieged with them in the king's palace, but would not fly away with them, was afterward slain by the seditious, we shall relate hereafter. However, Cestius sent Saul and his friends, at their own desire, to Achaia, to Nero, to inform him of the great distress they were in ...
Cf. 1 Thess. 2:14-16 and Php. 4:22:
You suffered from your own countrymen the very things they suffered from the Jews, who killed both the Lord Jesus and their own prophets, and drove us out as well ... As a result, they continue to heap up their sins to full capacity; the utmost wrath has come upon them.
All the saints greet you, especially those of Caesar’s household.
Both were violent thugs:
Ant. 20.9.4:
Costobarus also, and Saulus, did themselves get together a multitude of wicked wretches, and this because they were of the royal family; and so they obtained favor among them, because of their kindred to Agrippa; but still they used violence with the people, and were very ready to plunder those that were weaker than themselves.
Cf. Gal. 1:13:
For you have heard of my former way of life in Judaism, how severely I persecuted the church of God and tried to destroy it.
And both are never said to have returned to Jerusalem. As Andrew noted:
According to Romans 15 Paul is planning to visit Jerusalem and provide financial aid to the Christians at Jerusalem. This seems unlikely in the post 70 CE period.
And Saul is never referred to again after consulting with Nero in Greece in 66 CE. And if he was Paul then he could have learned about Nero's plan to send Vespasian to Judea and thus have known that "the utmost wrath has come upon them," as per 1 Thess. 2:16.
The experienced and unassuming general Vespasian was given the task, by Nero, of crushing the rebellion in Judaea province. Vespasian's son Titus was appointed as second-in-command. Given four legions and assisted by forces of King Agrippa II, Vespasian invaded Galilee in 67.
https://en.wikipedia.org/wiki/First_Jew ... 3Roman_War