The huge advantage for the AI in early expansion on deity really means that (maybe with some exceptions where they are really far away) an early rush is the way to go. Therefore, your first 2 cities should be production powerhouses to turn out the necessary units.
Founding city 2 (or 3, if map/land/AI allows it) near the metal is important.
I had one game where I could get 3 reasonable sites but had no metal.
I tried a chariot rush and I succeded because the AI had only a few spears.
In general, try only to take cities that will help you (ressources, good economic sites) and make peace. Than go into builder mode again until you are ready for the next expansion phase. As you are playing on deity, I will not explain the importancy of coordinating the war/diplo actions by cultivating friends, dogpile on someone throughout the game.
For me, this osziallting gameplay is the key on high levels.