Is the universe too complex to exist without God?

Believers will often point out to me that the universe as a whole, life in general, and humans in particular are far too complex to have come into existence naturally. 

I'm not sure how they know this as it's not as though they could have done any testing, experiments, or comparisons to know what can come into existence naturally and what can't. If a tree grows from a seed did it come into existence naturally or is it there only because God put it there? Maybe some god put together the designs for the wings of a butterfly, but no butterfly ever comes to earth fully formed. Is this natural, or design? 

It struck me one day that the argument above has a very big flaw in it and it lead me to tweet the following: 

Theist "humans are too complex to exist without a god" atheist "Is god more complex than people?" Theist "Yes" Atheist "In your own time..."

— MrOzAtheist (@MrOzAtheist) April 16, 2015

It seems to me that invoking a *more* complex being to explain the complexity of life or the universe fails to adequately explain what has happened. 

That god created the universe but is not subject to the laws we observe also relies on the special pleading fallacy. 

If God, far more complex than the universe, can exist without having been deliberately created, then why can't that apply to the universe itself? By their own reasoning, super complex things don't need to have been specifically created in order to exist, therefore the universe, which is far less complex than a god, can exist with no god required. 

To put it in mathematical terms (and I'm NO mathematician, so this might be pure nonsense)....

If maximum complexity = x and god's complexity is maximum, then god's complexity = x. 

The complexity of the universe is less than the complexity of god by an unknown factor. I'll call that factor f. 
The complexity of the universe = x - f. 

If a complexity of x requires no creator, then a complexity of x - f requires no creator. 

The same can apply to life, and humans. In either case the complexity is x - n where n is a varying amount, denoting the level of complexity lower than god's. Again if a complexity of x requires no creator, and complexity of x - n also requires no creator. 

A theist cannot believe a god to be more complex than people and not require a creator whilst simultaneously believing humans are too complex to have come into existence without a creator. 

If you can explain a god without a creator, you can explain a universe without a creator.