The Arab and Ottoman Empires invaded Europe from the East, repeatedly, which is actually what brought Classical literature back to Europe, triggering the Renaissance and leading to Europe going on an expansionist streak to fight back (and then for power and gold, of course).
Your lack of knowledge is shown by your generalizing over "the East", as if Indian, Japanese, Chinese, Arab, Persian, Turkish, Russian, and Byzantine empires all had some "essential Easternness" in common.
And then of course there's the issue that the Chinese Empire did have many expansionist periods, which were only really blocked from reaching Europe by such barriers as Mongolian armies preventing them reaching through Siberia and several different mountain ranges to their south and west, which were easier to trade through than to invade through. Oh, and of course we mustn't forget the Indian and Middle Eastern empires that would try to block a Chinese colonization of Europe on grounds that it was their turf.