Gave up several times on starting Persia without cheating (once I conquered Babylonia but India already had several spearmen in 3 cities). So instead of having my Hammurabi conquests go to waste, I decided to hand my empire over to Cyrus. Here's what happened:
1. Hammy builds Ashur (to flip Shush quicker) and beelines for archery.
2. Initial warrior goes to India after the goody hut for xp. Capture Delhi but don't raze it, instead build up infrastructure (roads/farms). Delhi has Hinduism but no Buddhism sometimes when you get there--it happened to me.
3. Build another warrior to go pick up money from huts west (this is crucial).
4. While archery is researched build barracks in Ashur. Shush builds worker to farm wheat.
5. Archers go to Egypt and capture Niwt-Rst (or whatever city is the capital).
6. Archers go to Greece and capture Athens. Greece founded Buddhism thankfully (otherwise I'll be one religion short). Don't build any more military.
7. Research mysticism, masonry, pottery. Workers build cottages around Ashur and Niwt-Rst.
8. Build Stonehenge in Niwt-Rst.
9. One turn before Cyrus appears, move all units in Ashur into Shush. Even in emperor mode, Cyrus is friendly so they will open borders without any gifts. The first city to give them should be Shush (it's the center of your empire and already connected to most of your other cities). I tried giving Athens first (thinking that I'll build Oracle) but I lost too much money without all those trade routes. Give all units to Cyrus. DON'T declare war on Cyrus (otherwise you'll lose next turn before you can switch)--I know, losing those free troops hurts, but your economy cannot support too many troops, so it's a blessing in disguise.
10. Switch to Cyrus next turn and capture Ashur. One settler to found Gwadar on the coast, and another to Artacoana in the north.
11. Civics should be hereditary rule and NOT slavery but serfdom. You need all those workers to build infrastructure ASAP.
12. Capture Jerusalem and Sur.
13. Research Meditation (for missionaries), Priesthood (for temples), Aesthetics (3 wonders) and maybe get Math from a great scientist. Most of the time your research will be close to 0-10% but you should get there in time. I decided not to go for construction because it only gives you Great Wall, where I needed more wonders for my expensive research.
14. Delhi builds Pyramids and Parthenon (make sure to build a temple first for hiring priests)
15. Athens builds Great Lighthouse. Because it's not connected to your capital, even if you have the marble quarried, you can't access it, so I got beat by China to the Oracle by 3 moves. If I had built more roads to Jerusalem I could have gotten the marble in time.
16. Shush starts with Temple of Artemis (use all tiles including the copper, marble and stone) and Shwedagon Paya later.
17. Gwadar builds workboats and harbor first, then Moai Statues as soon as possible. Statue of Zeus (from 4 free monuments from Pyramids) is built in 7 moves.
18. For your great priests, spawn them in Shush and Delhi. Spread your religions around so you can build temples. The one in Shush should be done first and sent to Athens. The other one will be born right near the end in Delhi with the help of the Parthenon (I had to reload several times to avoid a great engineer spawning due to Pyramids).
19. Ethiopia will vassalize which helps you not to have to build more cities in India. I tried to keep Samarkand several times but it was razed after I lost it twice to barbs. I finally got enough troops to rebuild Samarkand but it wasn't really necessary.
20. Note the conspicuous absence of Arabia in my cities. I did my usual trick with them--gave them Gordium (which I recaptured the same move) so all their initial units disappear. Then Sur and Jerusalem asks to flip to which I agree, having already loaded two galleys with troops and sailed away the move before, so I can recapture them the same move. Somehow San'a must have not been razed by the barbs because Arabia was still alive. But with the Temple of Zeus and 10 troops converging to the Levant Arabia sued for peace, and I even got Currency from them (I was 1 move from finishing it)!
21. Don't forget to build lots of axemen and spearmen in Egypt (to counter impi and camel archers), several spearmen in India (for the barb war elephants) and garrison spearmen in Samarkand (or fortify them in the forest north of Artacoana).
Cheating is hard.