well, that was the substance of my original reply, jomifl. I suspect the earliest Middle Eastern religion in the "western" world was Mithraism, carried by Roman soldiers, but as immigrants rather than invaders; Zoroastrianism may also have made its way west to some degree. Judaism spread by immigration; Islam is doing the same at the moment, after initially being carried by invasion. Christianity spread chiefly by proselytising and conversion.
I don't think invasion, even on a small scale, can be called "creeping"; conversion and immigration can. But they have both been going on for a very long time.