I'm not a Deity-Player but I've been able to win every different victory type on Emperor with CEP. The most important thing: you don't need to build settlers or workers so early. If you don't have settlers you don't need workers (no luxuries needed for positive happiness). Build a troop while researching Pottery, then either build a shrine or another troop and rush the shrine once you have the money.
Research Archery, Animal Husbandry up to Mathematics, on the way build the Temple of Artemis and Hanging Gardens. Meanwhile concentrate on finishing Tradition. The turn you have enough money rush a worker. With some luck you can even build the Pyramids afterwards so you get 2 free workers and don't have to build one. After that it all depends on how you want to play/win. I love having a religion that grants +2 faith/+2 tourism per world wonder but maybe that's just me. It definitely gives you a headstart for the culture victory.
Either way, once the Hanging Gardens are done you can go Petra if in desert or else get Calendar, Writing, Sailing. My next beeline is usually Physics for Notre Dame, Civil Service, then trying to build Forbidden Palace and be the first on the Printing Press for 4 votes in the world congress. If you get that and don't have too big a game you can use a diplomat to trade for a vote so you can make your religion the world religion which should ensure your diplomatic dominance throughout the midgame.
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