I never played Trebizond, but have played in this area with some tags (Theodoro, HisnKeyf, both Quounlyus and so on). So my strategy is only a guess, sorry for that.
I don't think it is wise to go for Georgia area (Imereti, Georgia, Samche, maybe even Circassia) too early, unless you can finish a war in the first 2/3 years (Imereti should be possible, I guess) Why? Because the Ottos will in nearly 100% wage war with Albania!
Get certain alliances you can at game-start, I think Karaman, Dulkadir will both be possible from the get-go. As Aq-Quonlyu will want your land, it could be possible to ally Quara-Quonlyu (Aq's natural arch-enemy).
My first moves would be: Ally 2 of Dulkadir, Ramazan, Karaman immediately (should be possible as most of them will like you at game-start, all 3 nearly impossible, due to internal rivalries) absolutely DON'T ally Theodoro (historical ally gamwise, but AI-Theodoro is as useless as they can get) Improve Relations with Albania from the get-go.
Your second diplomat should either get a claim on Imereti or improve with Quara, don't know what would be better. Watch Albania and its allies (if you are lucky, they will be even allied to Hungary, normally it's stuff like Serbia, Genoa and of course they are guaranteed by Venice (and their trede league). Also don't ally Byz, unless Byz has very strong allies (veryvery unlikely, though I have senn them with Aragon AND Castille as allies in January 1445, absolutely no idea how that was even possible). Usually, Byz is doomed and will be the Otto's 1st target.
With 2 (or luckily 3 alliances) on your side, the Ottos will at least not attack you immediately (at least I hope so, but I rarely have seen them go for Trebizond very early, it usually takes until around 1460 or so). Keep that Relations with Albania very high, but DON'T ally them yet. If you can manage AND finish a war with Imereti in the mean-time, please do so, you have to finish that war until 1447/early 1448. Army up to Fl (Maybe, if you can afford it, even 2-3 k more) When the Ottos declare on Albania, wait a little while (send ships to see coastal regiments and stuff like that) until the Otto troops are on the European side and THEN join the Alliance with Albania. Hopefully it should be possible to smash the Ottos. But keep in mind that you have to do a separate peace to secure your own territorial gains, in case of victory, as Albania will take lots for themselves, you don't need Albania anymore after that war, so ditch them afterwards. With a little bit of luck, you should now be able to ally the Mamluks, have a much bigger powerbase and weakened Ottos.
Good luck, pal
