The Kalam Cosmological Argument has as its first premise "Everything that begins

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The Kalam Cosmological Argument has as its first premise "Everything that begins to exist has a cause" (at least in the form I've heard it). Often examples of "chairs" or "people" are given for things that began to exist. But this seems to be a category error - the Universe did not begin to exist in the same way that a chair does. Indeed a chair doesn't "begin to exist" in that it was created from other things. So to me it sounds like the argument overstates its case with "everything that begins to exist" since the only thing that has begun to exist is, well, everything. One could restate this premise as "The universe began to exist" could it not? Is I missing something or is this what is meant by this argument? If so it seems to be more of an assumption than the inductive reasoning I hear it being used as (e.g. "you've never seen a chair 'pop into existence' have you?").