Just ignoring them is actually an option, they will take Byzantium but you can find a new home for your nation. Lower egypt or Serbian lands. Then return when their stacks have spread out and deminished.
One of my favorite games was with the Turkish, they are in a terrible starting position which can be improved and fortified, but the Mongols will still come and ruin most of your buildings anyway. Instead I immediately started a jihad against England, all of my generals and jihadists easily looted everything in their path on the way since it was so early in the game, and by the time I took London I had enough cash to rebuild there.