You are correct in that it is a question evolution cannot answer. It is also a question that intelligent design cannot answer either, therefore there is no refutation. Intelligent design is just a glorified thought experiment trying to come up a way to come up with a way to scientifically test for God. They are welcome to try, but I suspect they will be spinning their wheels for a good long t time. I still have yet to see a scientific paper that has been peer reviewed by other scientists in the field of evolutionary biology testing any tenets of ID theory. Until then, they are philosophers playing at being scientists.
You are correct in that it is a question evolution cannot answer. It is also a question that intelligent design cannot answer either, therefore there is no refutation
You do not need to have a competing theory in order to refute a theory. All you have to do is to show that the theory is false. If for example one could show that water runs uphill that would refute the theory of gravity even though there was no theory to explain such behavior. Indeed that is how science works. If a theory cannot answer the refutations, it is deemed false and research goes on for other explanations. Science does not say, we must have an answer to everything so even if a theory is wrong we will accept it until we can find a true one. Science rejects theories which are proven wrong. In fact accepting theories that are false is totally contrary to science and if science had followed your methodology we would still be riding horses.