Personally I don't see ahkbash at all, and they're a pretty rare breed in most countries, so its pretty unlikely you'd find one in a shelter. Even in areas with a lot of farms or even areas where livestock guardian dogs are common they are still a pretty rare breed, and they aren't a very common house pet for good reason- they're still usually bred as working dogs and most still retain all the things that make them great flock guardians, which do not tend to make them good house pets.
I would wager a guess that there's maybe some German Shepherd (possibly one of the white ones, or a "Swiss Shepherd"), maybe some Lab, maybe some Husky and a few other things in there. She looks pretty thoroughly mixed to me though. Breeds will become more obvious as she grows, its very hard to tell with puppies.
For size, going from perspective in the picture I would guess maybe medium to large. Probably not a small dog, given her apparent size at this age.
WOW! Is that pup ever cute! Hard to tell if her ears will stand up or not. It may be easier to guess once she's a little older. For now, all I can say is that she is gorgeous! @Moonstream Funny you say that rarer LGD's are never found in shelters. We pulled an Akbash/Kuvasz from a kill shelter and pulled a Kuvasz from animal control. I adopted an Anatolian Shepherd X through the rescue too. I know someone who got an Akbash/Maremma/Great Pyrenees puppy last year. There was someone that contacted the rescue about their sister's Akbash X who needed rescue. Very recently, there was a Tibetan Mastiff in a high-kill shelter. The rescue will be pulling a suspected Akbash X soon. I have seen plenty of Great Pyrenees mixes in various shelters as well. I think it depends more on where the OP is other than how rare a LGD is. I'm not trying to pick on you, just saying that any dog can be found in a shelter at some point no matter how uncommon they are.