Opening gates does not really count as luck. If you have several spies in the area you can insert just enough spies to guarantee the gates will be opened. A bit of saving and loading and you will know exactly what to do.

It should be possible to conquer the entire map by about 240-250 BC. That is with an unmodded EB game; as far as I am aware Fluvius plays with extended movement mod, which of course makes it a lot easier.

I managed to own about 54 settlements as SPQR by the end of turn 19 in an unmodded game.

The Seleukids are probably the best suited for a a rapid world domination game.