As Dawkins says: "A designer God cannot be used to explain organized complexity because any God capable of designing anything would have to be complex enough to demand the same kind of explanation in his own right."
Here is a counter-argument based on the hypothesis is that there's no logical connection between the structural complexity of a designer and the object being designed. We can analyze the hypothesis by considering the design of real systems (I've been involved with a few, maybe you have too).
- We know from the concept of structural decomposition, or stepwise refinement (e.g. in software or hardware) that a large design which cannot be comprehended in its entirety by its designer can nevertheless be produced if the designer factors the work into a number of simpler subdesigns; and these in turn can be factored until each particular job is comprehensible.
- We know there is, in principle, no upper limit to the complexity of the design that can be attempted in this matter, because we are looking at it from a top-down viewpoint, not bottom-up. In theory this means that given enough time or resources a designer really can design something more complex than him or herself.
- We know that there may be an upper limit practical complexity of a design that may be implemented which is governed by the methodology of the design process. In other words, more complex designs don't need a more complex design process, merely a more consistently applied methodology - ie the random factors that affect human beings in a normal environment undermine their ability to create complex designs.
AFAIK, the basic question about whether Evolution is a product of randomness or is determinism seems to have shifted over the past few decades. I distinctly remember in my youth (around 25 years ago) that evolutionists presented evolution as a series of random events subject to the process of natural selection. The important thing to emphasize was the 'randomness' of survival. In retrospect I conclude that this was the case, because it's a good argument against God - if randomness is the source of evolution then obviously it's under no-one's control, not even God's.
However, in the intervening decades we have a better estimation of how badly randomness works as a driver for evolution. And so the argument has shifted to looking at the natural selection side of evolution as a deterministic process. A deterministic process can also be used as an anti-God argument: if a process is deterministic, then there's no decisions for God to make.
This argument isn't really trying to weigh up these two viewpoints. All it's about is saying (a) that the complexity of the designer has no bearing on what is being designed in a situation where a designer is involved. (b) A designer's methodology does have a bearing on what can be designed - a methodology equivalent to a process of natural selection would be extremely counter-productive.