According to an acquaintance who works for Turkish on the 737 as an FO you get offered 777 after about 6 months. The only issue with Turkish is no upgrade if you don't have a 4 year degree. If you are Turkish though that may not be the case. A big word of warning on going to the ME or Far East is how to get back if you are not happy there. It's certainly not for everyone by all accounts. Good luck!