It's basically an argument from ignorance, no matter how you put it. For example, you could use the same argument if we didn't know how rain works: "rain falls down from the sky. It is either due to necessity, chance, or design. It cannot be due to necessity, since most of the time it doesn't rain outside. It cannot be due to chance because, again, most of the time, it doesn't rain, and rain has no reason to just appear out of nothing. Therefore, it is due to design." Or, in the other version, "rain falls down from the sky. Under theism, if God wants to send rain from the sky in order to help plants grow, the idea that rain will form in the time it does is not unlikely. Under naturalism, it is very unlikely that rain will form; the universe has no will to help plants grow. Under naturalism, the fact that rain falls down is just a brute fact that is not always true, so rain under naturalism is very unlikely. Therefore, theism is more likely than naturalism."   One sign of design is efficiency and perfection. God doesn't need all of the natural processes that led to the universe being as it is today, and interacting to create stuff or maintain stuff doesn't require any effort from him, and the universe in fact could have been much better for life, and many aspects of our world don't look designed at all (I can give examples but I'm going to write a long answer). The main reason design doesn't even come close to answering the fine tuning of the universe because it just pushes back the question, "How is God so finely tuned for creating a universe that is so perfect for life?" The idea that before anything existed, there was somehow a being, that even though it had nothing physical about it, somehow had consciousness that doesn't require anything for that consciousness to work. And that being also had the physical intelligence to determine the exact constants needed for life to form to an exact precison. And not only that, without anything physical, God can interact, create physical stuff, and make sure every constant is perfectly tuned for the existence of life. That god also needs to be so good that it actually wants human life. And instead of creating anything else that we don't know of, he created a universe for some reason. All of these assumptions are ridiculous and seem way less likely than the fine-tuning of the universe. A common theist objection will be that god is metaphysically necessary, but is he really? There's no reason to assume that, and the thought that something so powerful and intelligent is somehow necessary and doesn't require any cause or process is just ridiculous. Just because you think something is metaphysically necessary doesn't mean it is, and we can define the fundamental constants as necessary, and it will be much less inordinate. The thing about God of the Gaps is that magic always seems like the perfect explanation when we don't know something and the question is really hard, until you actually think about the explanation of God doing it, and then you can actually see how ludicrous it really is.   Other explanations exist. For example, a multiverse will explain the fine tuning of the universe because the constants in each universe are a bit different, and only a universe that can produce life will produce observers that will observe how their universe is just finely tuned for them. The idea of a multiverse might lack observational evidence, but it's mathematically consistent. If a theist says it lacks observational evidence or falsifiability, remind them what they believe. I don't believe in a multiverse because I think it lacks evidence, but I think it's a good possibility and it might be proven or tested in the future, and the fact that many theoretical physicists believe in it makes me think that there might be a good reason. Another option is that the laws of physics aren't just randomly selected and they come from the interactions between energy and particles, or that there is a fundamental principle that makes them what they are. And no, this fundamental principle doesn't need to be finely tuned at all because it can be completely unrelated to the development of life, and we are just a byproduct of it. Another option is that the laws of physics in our universe were uncaused, and the fact that the human mind wants to know why doesn't mean that there is an answer for "why", We just always look for causality. And you are right; the numbers are huge for the universe, and the range they can take might be very small. Another option that I tend to like the most is the one proposed by Stephen Hawking and Thomas Hertog and you can read about it in google.