Here's what I think actually happened, going from 3 books that are very informative. Professor Robert Eisenman's https://www.amazon.com/dp/B002JWD69Y/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1 , this book 'Creating Christ' https://www.amazon.com/Creating-Christ-Emperors-Invented-Christianity-ebook/dp/B01LRP3EDG and Judas of Nazareth https://www.amazon.com/dp/B00JGWFE9A/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1 .
To try to summarize all of it up, Christianity is basically a sham dreamed up by Paul, possibly a Roman agent, to infiltrate messianic Judaism and turn it from a violent movement trying to overthrow Roman rule of Jews into a peaceful religion, Christianity, that Rome could actually work with. The pro-Roman bent of the Gospels, the Jews saying 'His blood is on us and on our children', Pilate's sympathetic portrayal, and more point to pro-Roman if not outright Roman authorship.
Note also how the dating of the Gospels is after 70 AD, right after the first Jewish Roman war that destroyed the second temple and left Rome free to write history as they see fit. Note how even in the Acts of the Apostles text itself, Paul clearly has Herodian and strong Roman connections, enough that he can call on 470 Roman troops to escort him from Jerusalem to Caesaria.
Look at Paul's own words in the ending of the book of Philippians: "All the saints greet you, especially those of Caesar’s household."
Tacitus writing about Christus (which could have been Chrestus) may just have been about the latest messianic claimant at the time, and not an actual Jesus. The claim Chrestus was executed by Pilate was either an interpolation over Porcius Festus or possibly about Judas of Galilee, another likely self-proclaimed messiah, being crucified by Pilate.
Josephus didn't actually write about Jesus--the Testimonium Flavium is clearly a Christian interpolation since tons of Christian authors don't even mention it before the Middle Ages. Josephus did write about Judas of Galilee, a founder of what was called the Fourth Philosophy, part of a violent zealot movement to overthrow Rome.
Most of our Christianity comes from Paul, who was sowing discord among Judaism. Professor Eisenman identifies Paul as 'the liar' mentioned in the Dead Sea Scrolls. Paul has a fight with Peter and James at Antioch over eating with Gentiles, which leads to a discrepancy--if a real pro-Gentile Jesus existed, why didn't Paul just cite him to win his argument that eating with Gentiles was ok? Since he did not, it's clear the whole philosophy of the Gospels came AFTERWARDS, i.e. during the time after the first Jewish Roman war when pro-Romans were writing the Gospels to try to turn a violent Judaism into the peaceful Christianity that wouldn't fight back.
Pope Clement I is actually possibly Titus Flavius Clemens, a member of the Roman Imperial family! As was Saint Domitilla: https://en.wikipedia.org/wiki/Flavia_Domitilla_(saint) .
When the Flavians lost power to their kinsman Domitian, the project may have been forgotten. There is scant evidence that Christians were persecuted by Rome early on, and when later the actual persecution happened, the Roman origins of Christianity had already been lost.
There's no hard evidence Paul was actually beheaded as tradition claims, or if he was it may have been due to a shift in power as when Domitian killed the Flavians. And didn't anyone ever think how odd it was Paul had access to so much writing (when writing was rare and expensive) as a "prisoner"?
The peaceful Jesus character in the gospels was likely overlaid over an actual militant Jew who was crucified, possibly Judas of Galilee: https://thethreemessiahs.wordpress.com/2014/12/25/42-similarities-shared-by-jesus-and-judas-the-galilean/ .