No amount of complexity, specification, or information found in the universe could ever lead us to conclude that it was caused by a cosmic creator.
Why is that? If we found something like a tractor on another planet, we would conclude that it was created by an intelligence (wouldn't we?). So if we discover fine-tuning in the laws of nature, shouldn't we conclude that it was caused by God?
No. Because for every possible state of affairs we can think of (a universe with only hydrogen, a universe with only three atoms, etc.) we can also think of some peculiar spiritual being who would desire exactly that kind of universe to be created. A creator who wants a life-friendly universe is therefore just as improbable as the life-friendly universe he is called on to explain. In fact, he is more improbable, given the facts I've outlined here.
People bring up a lot of challenges to this argument. For example, isn't this just asking for "an explanation of the explanation"? No, it isn't. When you truly explain something you have to provide an explanation that is more likely than postulating simple chance to explain event X. If you do not, then lucky chance is a more likely cause of event X than is your explanation, and therefore, we cannot accept your explanation.
Another objection is the following: what if we found tractors on another planet? Would people like you refuse to attribute this to alien intelligence? Couldn't people like you just say,
"For every possible state of affairs we can think of (a planet with only hydrogen, a planet covered in silly string, etc.) we can also think of some peculiar alien being who would desire exactly that kind of planet. An alien who wants a tractor is therefore just as improbable as the tractor he is called on to explain."
No, I couldn't say that. And here's why: In this case, there is reason to think that alien with the desire to build a tractor would not be equally likely to the other nonsensical possibilities. And that reason is that we have tractors on earth, we use them for harvesting food (which we, and certainly every other living being, needs) and this provides us with some backround knowledge that increases the initial probability that creatures on other planets will do the same.
However, we can't really extrapolate like this to God (or any other spiritual being that might exist). Our backround knowledge about intelligent agents means essentially nothing in regard to God and other hypothetical spiritual beings. And that is because we are physical beings who evolved, while God is not a physical being and did not evolve. Our desires and our ways of thinking were determined by natural selection. God's (or other spiritual being's) thinking was determined by... Well, whatever it was determined by it couldn't have been a process of evolution, and we don't really have a clue what could determine it.