why not save a step...

It's true that "god" is a complex predicate, but so is any intelligent agent. When we see a purposeful arrangement of huge rocks in a field, we don't conclude that they arrived there by glacial action by arguing that intelligent action is "too complex". Rather, we consider how plausible it is that the configuration could result from natural processes and compare that to the known powers of intelligent action to enact complex designs.

Similarly, we can apply this same knowledge to Creation. The degree of intelligence necessary to produce the cosmology and life that we observe may significantly exceed that needed to pile up some rocks, but this is not a difference of kind. By comparison, the number of coincidences needed to arrive at the same result through unguided processes is, in the literal sense, incredible. Since material processes lack sufficiency as an explanation, we have only two options: give up and say that life has always existed, or consider alternate explanations.

Materialism is unwilling to accept either alternative. Now, we can probably agree that the first is genuinely not satisfactory, but the materialist has an a priori commitment to only accepting material explanations. The problem with this commitment is that it cannot be proven rationally; it is purely philosophical in nature, and therefore represents a limit on the materialist's ability to accurately understand reality.

instead of solving the problem, you now have something even more complicated to explain

Perhaps, though see other Answers mentioning the idea of divine simplicity. To wit, "god" is an entirely different category of brute fact to assume. In any rate, the real issue here is Münchhausen's Trilemma, which can be simplified as "no rationally consistent exploration of nature can be complete". Positing "god exists" does not need to halt investigation, however! Rather, positing "the universe (and life!) always existed" is not fulfilling because a self-existing universe is not the sort of thing one would be inclined to take as a brute fact. (It's also not consistent with the available evidence.)

I would also argue that it's an error to reject having something which cannot be fully explained. We don't fully understand quantum physics, yet we generally believe it to be useful. The history of science is chock full of phenomena we couldn't fully explain! (Indeed, one could argue that all of science is still in this state. What we have aren't so much explanations as models with predictive power, many of which increase in complexity as time goes on.) Similarly, if the evidence suggests the existence of god, that shouldn't preclude "god" as a useful hypothesis which can be further examined.

You may note I've used "god" with a lower-case 'g' throughout. This is because nothing in the Answer points to the Christian God, specifically. For that we need, as mentioned, a different investigative apparatus, which we have in the form of divine revelation and which is authenticated in consistency with natural evidence and by the miracle of Christ's Resurrection.

Why not save a step?

Nor should we be willing to accept "the universe" as a brute fact. As an explanation, it is profoundly unsatisfying. To steal the delightfully pithy rejoinder from pygosceles's Answer:

If you want a loaf of bread, I suppose a baker is an unnecessary and overly complicated extra step.

"The universe" is not a causal agent; rather, it is a thing which is in want of an explanation. By contrast, while it's true that "god" might be viewed as a complex predicate (although there are arguments against that; see "divine simplicity" as mentioned in other Answers), god is not the sort of predicate which demands a reason for its existence. As jaredad7 notes, there is a principle known as the Principle of Sufficient Reason which can be satisfied by "god", but not by "the universe".

In any case, the real issue here is Münchhausen's Trilemma, which can be simplified as "no rationally consistent exploration of nature can be complete". Either we must accept that an infinite regress of explanation is necessary, or we decree a First Cause as a starting point from which all else follows... and we have established that "the universe" is not a satisfactory First Cause. (Nor is positing it as such consistent with the available evidence, which strongly indicates a) that the universe had a beginning, and b) that life requires Design.)

To be fair, positing "god exists" isn't all that satisfactory of a resolution, though it we have shown it is superior to other possible stopping points. However, the existence of god needn't halt investigation! It does, however, offer us neat line which can be used to separate "natural" knowledge from metaphysical knowledge while suggesting that the methods used to examine the natural world may not be appropriate to "going further up the stack". Indeed, classical theism can rightly be seen as the study of god and as the proper companion to natural philosophy (that is, what we now call "science").

Why accept "god"?

Intelligent agents have known and demonstrated causal powers. When we see a purposeful arrangement of huge rocks in a field, we don't conclude that they arrived there by glacial action by arguing that intelligent action is "too complex". Rather, we consider how plausible it is that the configuration could result from natural processes and compare that to the known powers of intelligent action to enact complex designs.

Arguing that "a Designer is too complex" or "a Designer can't be explained" is a philosophical objection, not a rational one. The postulated god may be complex or unexplainable, but these attributes don't disprove god's existence. (Strictly speaking, it is impossible to disprove the existence of god, but we can and should consider whether god acted — in a supernatural manner — with respect to some event or circumstance. When doing so, we prefer a natural explanation, but when nature is shown to have insufficient causal power, the correct action is to consider alternate causes.) Indeed, not only is the history of science abounding with examples of things believed correct despite inadequate explanations, in a sense the entire field consists not of explanations, but merely of predictive models. Moreover, the complexity of these models tends to increase over time!

When we recognize that setting "god" aside in a box labeled "not science" is, in fact, not scientific at all, but wholly philosophical, we can properly investigate whether "god" — or, more accurately, "supernatural intervention" — is a likely explanation for what we observe.

For most things, natural laws suffice, but natural laws fail to explain life or the fine-tuned universe (among other things). These specific examples, however, are explainable by Design. The degree of intelligence necessary to produce these may significantly exceed that needed to pile up some rocks, and may be difficult or even impossible for us to comprehend, but this is not a difference of kind. By comparison, the number of coincidences needed to arrive at the same result through unguided processes is, in the literal sense, incredible. Natural processes lack sufficiency as an explanation.

At this point, the rational options would be to either decide that life and the universe have no cause, or to accept that their cause is supernatural. Now, we can probably agree that the first is genuinely not satisfactory, and Materialism, having an a priori commitment to only accepting material explanations, is unwilling to accept the second. This commitment, however, is not rational but philosophical, and since its axiom cannot be proven, it represents a potential (and, as it happens, actual) limit on the materialist's ability to accurately understand reality.

Who is "god"?

Readers may note I've used "god" with a lower-case 'g' throughout. This is because nothing in the Answer so far points to the Christian God, specifically.

If one assumes "god" is the First Cause, several inferences are possible (a la Romans 1:20); tnknepp gives us a list. To go deeper, however, requires (as previously noted) a different investigative apparatus and a different set of observations. To wit, it would be incredibly helpful if we had any directly-imparted knowledge or eyewitness testimony... and, as it happens, we do! Rather than remaining aloof from His Creation, God has revealed Himself to us in the form of Scripture, authenticated in its consistency with natural evidence and by the miracle of Christ's Resurrection.

It's amusing that a materialist would make such an argument when "god of the gaps" is one of the more frequent criticisms leveled against deists. To halt investigation simply because it is difficult is not how one goes about obtaining Truth. To simply say "the universe always existed" is to explicitly and deliberately halt one's search for knowledge.

Materialism is unwilling to accept either alternative. Now, we can probably agree that the first is genuinely not satisfactory, but the materialist has an a priori commitment to only accepting material explanations. The problem with this commitment is that it cannot be proven rationally; it is purely philosophical in nature, and therefore represents a limit on the materialist's ability to accurately understand reality.

It's amusing that a materialist would make such an argument when "god of the gaps" is one of the more frequent criticisms leveled against deists. To halt investigation simply because it is difficult is not how one goes about obtaining Truth. Sure, one can say "the universe always existed" (a form of animism!), but doing so is to explicitly and deliberately halt one's search for knowledge, essentially drawing a line in the sand that says "no investigation is allowed beyond this point". As this is exactly what materialists love to accuse deists of doing, to deliberately employ the technique themselves is hypocritical. (And, if we're being honest, the incredible fairy tales that materialists invent to explain the universe show that they aren't willing to make such a statement.)

Materialism is unwilling to accept either alternative. Now, we can probably agree that the first is genuinely not satisfactory, but the materialist has an a priori commitment to only accepting material explanations. The problem with this commitment is that it cannot be proven rationally; it is purely philosophical in nature, and therefore represents a limit on the materialist's ability to accurately understand reality.

instead of solving the problem, you now have something even more complicated to explain

Perhaps, though see other Answers mentioning the idea of divine simplicity. To wit, "god" is an entirely different category of brute fact to assume. In any rate, the real issue here is Münchhausen's Trilemma, which can be simplified as "no rationally consistent exploration of nature can be complete". Positing "god exists" does not need to halt investigation, however! Rather, positing "the universe (and life!) always existed" is not fulfilling because a self-existing universe is not the sort of thing one would be inclined to take as a brute fact. (It's also not consistent with the available evidence.)

I would also argue that it's an error to reject having something which cannot be fully explained. We don't fully understand quantum physics, yet we generally believe it to be useful. The history of science is chock full of phenomena we couldn't fully explain! (Indeed, one could argue that all of science is still in this state. What we have aren't so much explanations as models with predictive power, many of which increase in complexity as time goes on.) Similarly, if the evidence suggests the existence of god, that shouldn't preclude "god" as a useful hypothesis which can be further examined.

You may note I've used "god" with a lower-case 'g' throughout. This is because nothing in the Answer points to the Christian God, specifically. For that we need, as mentioned, a different investigative apparatus, which we have in the form of divine revelation and which is authenticated in consistency with natural evidence and by the miracle of Christ's Resurrection.