The issue is you believe everything was made by god, whether complex or not, so it doesn't matter how complex something is, because even if it isn't complex you say it was made by god. This renders the complexity argument as redundant and your use of complexity as meaningless.
But what the bible points to is a being that transcends the complexity that we see here. Complexity actually becomes something entirely different in another dimension. So to speak in terms of complexity of life on earth is not the same as saying that God is complex (which I believe He must be). But organism complexity is relative, because even the single cell is a very complex thing.
So life starts at complex and just gets more complex and fascinating. I would not intuitively look at life, especially with the microbiological advances of today, and think "oh all this is happening on it's own without any instruction". I've got to think that these life forms, from the least to the greatest of complex organisms, have been infused with a software program to drive them to do what they do. It doesn't make sense otherwise. If that "software" is really there, then it makes perfect sense to wonder about the intelligence who coded the organism.
So my point is that if a person believes that there is at least a possibility of intelligent design behind all this, it opens the door to the possibility of what many call God. Atheism shuts down that possibility right from the start (so it seems).
I base this on the idea that god is also a soul/spirit. If god has always existed, then he can't be complex because complexity points to a deisgner. Therefore, a soul/spirit cannot be complex. However, you believe soul/spirits are created by god, so even when we point to something that isn't complex, you still see need for a desginer.
The idea is that God is eternal and operates in a dimension very different than this dimension where we are defining complexity. Therefore the idea that God cannot be complex because He wasn't created, is an invalid argument outside of this dimension.
But to keep it simple, if God is who the bible says He is, then He has always existed and was not created. If then, He is the Author of creation, then He made the rules, and is not bound by the rules or laws of nature that we observe in this dimension.