I would recommend instead of making them at war right from the get go have it be a branch of the focus tree for Byzantium. Preferably something near the top so that it can be done still early. Also might want to have an event chain that leads the two to war and if they haven't gotten that focus finished yet it will start the war off with Turkey getting a nice boost showing that they were allowed to prepare for the war. Just my 2 cents.

I think that instead of focusing on war with the turk it should be more of a expanding the power base type thing where they pupet Romania attack Bulgaria pupet the turks and generally lead a coalition of pupeted balkan states against Italy and try to reclaim their former land.

I doubt that realistically the war would still be raging in '36. Neither country actually had the resources, manpower and unity to keep at it for nearly two decades. Or exactly two decades if it's still going in '39.

Plus, as a personal preference, I like to start in '36 precisely to have some time to prepare for war. Starting directly with one isn't all that great for me even with Italy. And in Italy's case at least you start with pretty much a curb-stomp war against a much weaker power. Starting directly in a war with a worthy opponent... well, there's only so many times you can go to Valhalla before it gets old. In fact, exactly once, if Norse myths are to be believed ;)

I would say leave it as a buildup, but perhaps maybe have it not at the very top? As in, base it around buildup and invasion of Bulgaria, maybe? But also an event tree for those who just want Turkey and don't care about the other nations as well?

I suppose a focus tree would also work, since Byzantium will need those anyway. You could have something like a rebuild the eastern empire tree, with retaking Anatolia as the next node after root. So in 140 days, you could have a war-goal on Turkey, if you want to rush it.

I think it best if war they start at peace, preparing for war. War starts inevitably but triggered by events ?cypriot independence from Britain followed by Turkish invasion 30 years earlier than it actually happened!

Maybe make a national focus early on that gives you an event where you demand eastern anatolia or war like sudentland