I've played the first 100 to 150 turns several times, trying to figure out how y'all are doing it.
I am playing my fourth game, I conquered the island on T114, same time as a previous run.
Rome before T50, is possible with 3 archers and a spearman / warrior, and either a captured settler from Rome, or one of your workers.
Make a trap for the city defence, dangle a worker, the defender will claim it, kill it with the 3 archers, or better still do enough damage to take it easily with your melee unit. The melee unit should be at less than full hit points. Then the city defence will target it. 3 archers, not taking hits from the city, is enough for Rome.
Then, probably best to upgrade to comp bows. My army was 5 comp bows, a spearman (upgrade from ruin) 3 workers! and a scout. I took Greece next. If you are early, Shoshone are easy. I aborted a game where i prioritized science, and Shoshone built the Gt Wall when I was deep into their land and took my army out with comp bows. In my current game, they had developed mines to the north of the city and I placed comp bows on them with workers, 1 turn repair, pillaging for health recovery. Its possible to pillage twice a turn if needed. This is a bit of cheat, but Constantinople is also a walk in using this strategy. 114 turns for Rome, Athens, Moson Khani and Constantinople. Maybe the odd other city for access.
I bought 2 triremes and 2 scouts to explore once I had optics. Lots of ruins out there which are always handy.
In my current game I did not go for crossbows, but went full naval.
As for early game, I pumped out archers after a monument, then caught up with infrastructure. This game I built great library and Pyramids.
Policy wise, I went full Liberty, the 3 MOV's will upgrade archers to comp bows and then buy Galleass. Then I went exploration and into commerce. The Honor policy is not needed or beneficial in this game if you rush early.
I did pause before Greece to get Comp bows, then went GL, free tech to Philosophy and NC.
Early priority is archery and then construction, then Galleass.
That's how I played it anyway. I might be in for a fast finish time this fourth game, Its turn 118 and I am about to attack Poland with the fleet, 5 Galleass and a trireme. In this game something seems to have happened to Poland and Indonesia, both are way behind where they were in my other 2 games.