It would require luck to eliminate Rome before the end of Classical era, which means they would have to not settle many cities. In my game they managed to settle 4, I took 3 of them, kept 2 (Rome and their holy city which spawned a prophet JUST as I capped Rome, unlucky) and burned one, left them with one city which I destroyed later on. Early game was Full Liberty into Full Honor into Commerce and Rationalism. Honor is a really good idea on this map. Greece were strong players, and I had a DoF going but just as I was about to attack them from the Aegean sea with Ottomans, they both denounce me and I lost 3 points there
At that point, the military CS started giving me Keshiks which I used to clear the inland cities and eventually leave them with a pair of cities. My happiness was an issue so I opened Patronage for FP but Greece ended up building it for me so I captured it in Sparta, and had Germany take their last city. I used that later to liberate them and secure votes in the Congress
while buying all city states and burning down cities on the fly.
Early game consisted mostly of grabbing locations, beeline Wheel to activate my UA and Pantheon, then Horseback riding and Mathematics for Elephants and Catapults to attack Rome quickly while they are off against Greece.
Mid game consisted of consolidating happiness and exploring further East while assembling a fleet. By then I have moved my main army back to assault Morocco. I took Panama so that I can access the Red Sea from the Mediterranean and attack Mecca. I was one turn too late in capturing. Meanwhile in Northwestern Africa, I rushed Physics and Chivalry and get Knights and Trebs up. Morocco did put up a slight fight but I took their cap and left them alone. They had Machu built which was the best thing about it
Then I upgraded Trebs to Cannons and invaded Spain with it. Once I cleared them out, I sent Inquisitors to remove
kebab Catholicism like I removed Buddhism from Rome beforehand. At this point my science started to roll and I pushed towards Schools first and then Cavalry and Artillery next. I cleared out most of the barbs at this point and focused more on city states. I passed World Religion but couldn't Embargo France for extra points.
Late game consisted of assembling a big enough force to attack Germany from the land and sea, my Frigates did really well in eliminating all coastal cities and ended with Range and Logistics. My Quins became Caravels and then Ironclads. I removed Germany but I was at war with ALL of the AIs at once save Greece. Russia were too far, and Morocco, Ottomans and Arabs were pushovers. Arabia settled many really crap cities all around Mecca, so I should have murdered Medina back when it was their only city remaining.
Conclusion I have all city states now, World Religion, World Ideology, FP, I have restored Greece, and sent Diplomats away since I am at peace with everyone now. Wait out 15-ish turns and get an easy Diplomatic Victory