There is so much complexity in the universe. It must have been designed and created by an intelligent being that is more or less all-powerful and all-knowing. This is the best explanation for the existence of the cosmos – God did it
If that is true, then who designed and created the designer and creator?
Nobody; God has always existed
You have not explained anything. You invoked God to explain the existence of the cosmos, but you have not explained the existence of God. To postulate a designer begs the question. So, you have failed to overcome my objection.
No, I have not failed; I said that God has always existed.
How do you know? If you can just claim that God has always existed, then I can just claim that the universe has always existed. But you would not accept that explanation, so why should I accept the "God did it"-explanation?
I don't know. I just have faith.
The “who designed the designer” objection is easy to overcome. If we required that an explanation must itself be explained it would lead to an infinite regress, and thus, we would never be able to explain anything.
This is not how philosophy and science works. For example, Ludwig Boltzmann explained heat by postulating tiny, unobserved particles (atoms). Boltzmann's theory was superior to earlier theories of heat, even though his explanation was itself unexplained.
Many successful explanations raise new puzzles and present us with new questions to be answered. So, explanations need not themselves be understood. I may understand why you didn't come to the party if you explain you got a headache, even if I have no idea how to explain headaches.
The atheistic objection is not fatal to theism because it misses the point. It is correct that “God did it” is generally a very bad explanation for anything. But, the “God did it”-explanation does not fail because theism has no good explanation for this explanation.
The problem with the “God did it”-explanation is that it is very implausible. It fails to provide almost everything that good explanations do. For example, it has poor consistency with background knowledge and poor explanatory scope.
So, when theists claim that “God did it” is the best explanation for some phenomena, the atheist's response should be, “Why is God the best explanation for that? Will you explain, please?”
Lipton, P. (2004). Inference to the Best Explanation
Dawes, G. W. (2009). Theism and Explanation