Christianity was formed as an eastern religion, so surely you'd need eastern traits.
Christianity also came to rise because the whole surrounding of its birthplace was Rome. It was irrelevant that the name and place was the Roman Empire. Any massive empire that seemed ruthless and oppressive to the common folk of the conquered would do.
Now, in your map, there's no such thing. There's Babylon, which I would assume has a similar type of religion. So what you need in your timeline is maybe the fall of Babylon and its conquest from Egypt or
@Graf Zeppelin , though ideally it would be Epirus, Hellas or Etruria as they're closer to Rome in terms of culture. But both seem farfetched at the time.
Could Christianity (or a similar religion) pop up in Etruria, Hellas or Epirus? Highly unlikely. It would require massive waves of immigrations from the East.
What could emerge would be a similar minded religion, but with Germanic (most probably) or Celtic elements, from within Etruria's borders. But Christiniaty spread because Rome was so dominant in the European world that everyone who followed wanted to be like Rome. And Christianity was something that could link them with that Roman allure, so every new random kingdom wanted to also be Christian to be part of this group.
Your Etruria is vast, but not rich enough and has no link with a great ancient civilization. Other than itself. Only Babylon has this to an extent, the rest of your big empires/states are not expanded well enough to attract influence from other peoples.
And the four pillars of the rise of Christianity was simply following the complete opposites of the four pillars of the Roman Empire, that by the time Christianity was emerging, there was no physical force on earth that could undo their Empire. Chrsitianity came and flipped Rome upside down. These four pillars of Rome were:
Strength (Christianity preaches Weakness, whereas Rome had Force, Army, Violence)
Wealth (Christianity preaches "mental wealth" and that material goods are meaningless)
Science (Christianity preaches "I am the word, follow me and don't search for anything else" and "ignorance is bliss")
Eroticism (Christianity preaches Fasting and Prudence, while Rome celebrated Arts, Beauty, Sex, Sports - mostly in the nude I remind you - etc)
Based on this, you can easily see that any vast and invincible empire could have this revolutionary internal uprising that will turn it upside down. But it'd be different and probably not survive if its place of birth was not self-sufficient. So if it starts in your Babylon and then Lidya or Egypt sweeps them through, it probably won't survive. Christianity needed the stablity that Rome provided to grow and mature as a religion and gain a formal following other than a bunch of angry mobs in urban areas.