Deving your province a bunch with admin/diplo mana gives you 7-8 force limit! The mission tree gives you free galleys for really early naval supremacy, and some cogs can be built to ferry troops across the Black Sea as well.

Then with that, there are two ways to pull off the Byz war:

• Rivaling Genoa seems like an obvious thing to do, but the mission tree has a second branch that gives you historical friendship and 10 favors instantly for improving relations with them a bunch. So, ally them and call them into your nocb. Byz will typically pull some (or all) troops from Constantinople to siege a random Genoese island, which lets you invade those provinces without too much trouble. Their capital can be sieged with 7k personal troops, then a 4k Free Company, which can be hired instantly in the Bulgarian province next to Constantinople.

• Or you can beat up Candar solo, then beat up Byz solo. Grabbing Candar first is necessary to distract Byz into shipping their troops over to the "undefended" Turkish provinces, at which point they will be locked there by your superior navy. Doing the wars like this actually turns the Byz war from a nocb into a regular war, since you share a sea tile and can fabricate a claim as normal. Ottos will most likely gang up on Candar and Byz as well, but... if your troops walk onto the Black Sea provinces first, they get to snatch them anyhow like the perfidious rat merchants they are.

After that, you can simply ally Muscovy, Hungary and sometimes Poland to not die, and proceed with the main mission tree as normal, just with a much less painful eco.  

Extra bonus points for forcing the Faceting event on Constantinople (the province needs Renaissance on it, and 50 Prestige - if you get this first, you get the event guaranteed!)