Your infinite-regress argument would be entirely sensible if someone were claiming that all code written without testing it is entirely broken. Fortunately, no one is claiming that. In view of which, what you say is just like this: "How do you know that your reasoning about what the code needs to do is right unless you've checked your reasoning? And then how do you know your checking of your reasoning is correct unless you've checked that? Etc., etc., etc. Therefore, no one is really developing software by thinking about it."
TDD is not supposed to be an alternative to writing good, clean code, inspecting it and testing it. It's supposed to be a way of writing good, clean code. (No, that doesn't mean it's supposed to enable idiots to do that, or supposed to make it effortless.) Maybe it works well -- i.e., enables a person with a given amount of brainpower and a given amount of training and experience to expend a given level of effort and get better code -- and maybe it doesn't; but the objections you've made here don't make any sense.