Eh, I didn't want to defend the argument but you're misunderstanding it and I'd just like to clarify what the position actually says.
People who properly hold the position would probably take a William Lane Craig approach of saying "Everything that begins to exist has a cause", which of course would not include God. The statement "something can't come from nothing" also only applies to things that have a beginning, if God always existed, there was no point in time where there was a 'nothing' that He had to come from.
And if there is an uncaused cause, you're right it doesn't have to be a specific God, not necessarily the Christian one, but based on a series of deductions it is said to have god-like qualities, and so maybe it is a "Cosmic Giraffe" but you'd have to concede a god-like being existed and caused all things.
The universe can't be the cause because the universe doesn't cause itself, and is argued it must have had a beginning, based both on philosophy (problem of infinities going into the past) and science (current big bang cosmology supporting a definitive beginning of the known universe)