Is there a flaw in reasoning here?

A: "Our universe as we know it, arose by natural means, or eternally pre-existed."

B : "No, it is so complex, it must have been created by God."

A : "If you try to find a solution for a complexity that you can't yet explain or understand, then it makes no sense to offer as a solution something of even greater complexity that you understand even less. Not only are you no nearer a solution to the initial problem, you have simply added another greater problem."

The statement: “No, it is so complex, it must have been created by God.”

In essence, B is saying it (the universe) is unknowable because it is so complex. While the discussion could easily revolve around the Argument from Ignorance (appeal to ignorance, argumentum ad ignorantiam), because it assumes a claim is true (or false) because it has not been proven false (true) or cannot be proven false (true) or the Argument from Incredulity, (the Divine Fallacy), which is “I cannot imagine how this could be true, therefore it must be false.” But I think a deeper analysis is in order.

To be unknowable is different from unknown. Unknown merely means something not known at present or not known to you. But unknowable means that which can never be known. Unknowable is that which, by its nature, cannot be known. 

The first hurdle is to define both the universe and God. Beyond that, to focus only on the universe aspect, they must explain how do they know the universe is “so complex?” To claim this, they already know something about the universe: it is so complex. Yet to know something about the complexity is to have knowledge, and that alone contradicts the proposition. Beyond that, they have to adduce evidence to support the proposition. The old Burden of Proof rule rears its reasonable head again. 

A: "Our universe as we know it, arose by natural means, or eternally pre-existed." 

Unsupported claim. Why not created by alien? We don't know the possibilities, so we can't necessarily call it a false dilemma , but we also can't claim those as the only two options.

B : "No, it is so complex, it must have been created by God." 

Another unsupported claim (and unreasonable).

A : "If you try to find a solution...

Except for the believers in magic (or gods that use magic), the magic is a presupposition that needs no explanation. To them, this won't be convincing, but to a science-minded individual that seeks explanation (not taking things on "faith") it does make sense.

B : "No, it is so complex, it must have been created by God."

This does not follow. Something may be complex. That only means it's multifaceted and probably hard to understand intuitively, maybe even at all. It doesn't imply Big G put it together anymore than it implies Cthulhu did.

I've said 'weak argument' because this needs to be fleshed out more.

A : "If you try to find a solution for a complexity that you can't yet explain or understand, then it makes no sense to offer as a solution something of even greater complexity that you understand even less. Not only are you no nearer a solution to the initial problem, you have simply added another greater problem."

I'm guessing the 'complexity that you [person B] cannot yet explain' is the origin of the universe, and the solution of 'even greater complexity' is God...but I'm not fully understanding this part.

B : "No, it is so complex, it must have been created by God.

The complexity argument to support the basis for the existnce of god has a long and solid basis in philisophical discussions and literature and, as far as I am convderned, it is never been refuted.