That logic does work when we're talking about evolution, for example. Creationists make the mistake of claiming that the odds that a particular critter could have evolved a particular way are extremely small, so there must be a god. But particular critters aren't the goal of evolution. Evolution is going to evolve critters in some direction.
But the odds that an interesting universe could have developed, such as one that can evolve life, with only one attempt, are extremely small. Not all outcomes are in the same category. Our universe is in the category of a very interesting universe, which would be extremely rare if created by pure chance.
When you see an identifiable pattern on an old analog TV set you know that a signal was sent from some place. That pattern will not be there by pure chance. There are a huge number of ways to create a pattern on a TV (the vast majority of patterns are just static), but an identifiable pattern needs an explanation, unlike pure static.
From my selfish perspective, it is legitimate for me to contemplate what version of reality gives me the best odds of existing: one where my odds of existing are next to zero or a version of reality where my odds of existing are quite good. I think it is obvious that the version of reality where my odds of existing are next to zero can pretty much be eliminated.
Some people seem to have a faith-based version of reality where they accept a certain version of reality, even when shown that their version of reality is virtually impossible, and their version of reality violates everything we know about nature. (nature doesn't make things in ones, for example) Nature is giving us clues. Many of the best scientists believe an explanation is needed.