I bet that dog will be huge, if a four week old puppy is that size already.
My suggestion is to get a large breed puppy kibble and supplement with a table spoon or so of cottage cheese and maybe some green cow tripe (but only a little).
I'd go with Fromm's Gold Large Breed Puppy, because I've seen what Fromm's can do for a dog first hand. Plus, it's easy to digest and is a good "allergy" food.
I've seen puppies go as early as 6 weeks from working lines, but that's not so common here. I'm not sure how to advise you to get socialization for your puppy.
I know that there are breeders who will email the sammy list and say, "Singleton litter- my puppy is 3 weeks and needs other puppies to play with. Can your bitch take her for a day?"
And because all of the breeders know eachother, this is a common practice to make sure that the little one gets that socialization.