I've discussed this topic before, but I'm stimulated by various things to consider this again. To begin, the believer line of reasoning goes something like the following:
When you see a building, you know it had a builder. When you see a painting, you know it had a painter. When you see the Universe, you know it had a creator. This is God. It's impossible for something to just come from nothing!
One rational response goes:
A builder takes existing materials such as bricks and concrete and re-arranges these to make a building. A painter takes existing materials such as paints and canvas and re-arranges these to make a painting. What existing materials did God use to make a Universe? You mean he made a Universe out of nothing? Didn't you just say "It's impossible for something to just come from nothing!"?
This response negates the argument by showing its internal inconsistency.
A typical response to such a negation is that "God" can in fact create something from nothing. The believer following this line of "reasoning" is implicitly assuming that the deity is supernatural - that is, s/he/it doesn't have to follow the very laws of the Universe that s/he/it (pronounced 'shee-it') created! I've encountered pushback from some believers on the notion that the deity is supernatural (for various reasons), but if you make this argument - that is, the so-called watchmaker analogy - then s/he/it must be capable of supernatural (i.e., outside of the natural laws of the Universe) deeds. S/he/it is capable of doing what nature cannot do. Indeed, if you also accept the omnipotence of the deity, then there simply can be no limits on what s/he/it can do.
I've argued in the past that the imposition of the God Hypothesis to explain the complexities of the Universe is both unnecessary and fundamentally useless, as it explains precisely nothing! What value does it provide for understanding the origins of a watch to "explain" its existence by invoking nothing more than the name of the putative watchmaker (say, Rolex)? Even if the hypothesis were true (i.e., the watch was made by Rolex), this manages to say nothing of how the watch came into existence from raw materials or upon what physical principles it operates to keep time. This form of mythical, supernatural 'explanation' is just what primitive people used to try to understand what we now know are entirely natural processes (thunderstorms, earthquakes, tsunamis, etc.). We now use science to explain many of those processes, and the gaps left for the s/he/it as an 'explanation' keep shrinking with time.
A key flaw in this fallacious builder (or watchmaker) argument for the existence of the deity is that if a deity created the Universe, who or what created the deity? This is related to the notion (above) regarding the supernatural capabilities of said deity. A common response is to claim that s/he/it exists entirely independently of space and time - the ultimate in universality. A convenient escape hatch, this one, as it's utterly unverifiable and, if accepted, negates the possibility of any counter-argument. This is an example of a deus ex machina - generally regarded as about as weak an argument as is possible to make, reminiscent of the famous cartoon by Sidney Harris in the New Yorker magazine.
Invoking a deity to explain the complexity of the Universe (or anything else) ignores the evident reality that the laws of the Universe permit certain forms of self-organization. As a meteorologist, for instance, I know that weather doesn't happen randomly, but organizes itself into weather systems at various scales. Such weather systems are governed by natural laws pertaining to the atmosphere. Other examples in other sciences can be cited, of course. Complexity "emerges" from simplicity precisely because of those laws of nature! It happens all the time, so there's no obvious need to infer the existence of a deity to explain all the complexity we see. Science can't explain everything, and makes no effort to deny that - whereas believers in a universal, supernatural deity think they can 'explain' everything by attributing it all to their chosen (mythical) entity.
Finally, another discipline of which the believers in the God Hypothesis seem to know little or nothing is quantum physics. I'm no expert, but I know that it's entirely consistent with the laws of quantum mechanics for something to appear out of nothing. In fact, it happens all the time, all around us. Although such quantum fluctuations generally have little impact on the macroscale world we sense with our human senses, this doesn't preclude that quantum fluctuations could have had a huge impact at the time of, say, the so-called Big Bang.
At this point, such an explanation for the origin of the cosmos as a quantum fluctuation remains unverifiable and so is just speculation, but it's at least not inconsistent with the natural laws of the universe (as we now know them). A supernatural deity is, virtually by definition, inconsistent with those natural laws! Claims for the existence of such a deity are, in fact, utterly inconsistent with science.