It is obvious that your question only applies to 'designers' that are constrained by the dimension of time. (i.e., 'natural designers' such as evolution, extraterrestrials, etc.) Further, you can only exclude an 'unconstrained designer' by assuming naturalism 'a priori'; but that is a philosophical choice, not a logical conclusion.
IOW... while you have designed your question to appear logical it is actually firmly rooted in fallacy.
Make sense?
The ex cathedra claim that a designer is required is also a priori, and by that standard has nothing to do with logic.
The Religion forum here on FR is the best place to have those kinds of discussions.
Not the least bit of sense, but thanks for trying.