A force which cannot be detected is indistinguishable from a force that's entirely fictitious.
Which makes said proposed designer indistinguishable from something that doesn't exist.
I wouldn't call that a paradox. After all, if said proposed designer had measurable properties, there'd be no issue in testing it.
Lol, what? Evolution is testable, which is why it is a part of science. You just went through why intelligent design isn't allowed (and correctly assessed it), but then you act as if a person couldn't just say "I believe in god", despite admitting that said deity cannot be tested. I'm very confused about your logic.
-_- I'm literally running an evolution experiment right now. I even designed the experiment such that other people without any special equipment could replicate it.
A sad fact is that evolution is a slow process, and anything that would speed it up fast enough for you to observe a transition on the scale of a lizard population evolving into a bird population would defy perimeters in nature so much that people like you would say it doesn't count as evidence. For example, it is entirely possible to increase the rate of mutation within genomes, and forced mutation is part of how people find out the function of genes. However, despite the fact that these forced mutations can be equally random to natural ones, the fact that they occurred due to human intervention would make people cry out "intelligent design". Which is as annoying as a person demanding that the circumference of the planet has to be measured with a ruler.