One need not fully understand the origin or identity of the designer to determine whether an object was designed. Thus, the question of the origin of the designer is irrelevant to whether we can detect design, the core focus of intelligent design theory. For example, if SETI were to detect a signal from an intelligent extra-terrestrial civilization, we would need not know how that life form arose to determine that there was indeed an intelligent entity that sent the signal. The question of the origin of the designer may be an interesting question, but answering this question is irrelevant to whether we can detect design.
The question "Who designed the designer?" is most likely a philosophical / religious question that lies outside the domain of scientific inquiry, and thus is beyond the scope of intelligent design. Religious objections require religious answers. In that regard, many religions have proposed ideas about the origin of the designer. For example, Christianity postulates the that the designer is God who by definition is eternally existent and has no origin. This is akin to Aristotle's 'unmoved mover" -- an uncaused cause. Postulating an uncaused cause is no philosophical problem, however, because every worldview has at its base an uncaused cause. Atheism/materialism, for instance, requires that the universe (or the chain of events that led to our universe) ultimately happened for no reason, just by chance. At its base, atheism proposes an uncaused cause. The right question is not "Is it a problem that Christianity has at its base an uncaused cause (God)?" because every worldview has at its base an uncaused cause. The right question asks: "Since every worldview has at its base an uncaused cause, whose uncaused cause is most reasonable?"
Because we have no experience with something coming from nothing, or with blind and unguided causes creating complex and specified information we find in our universe, atheism's "uncaused cause" fails. However, we do have experience with such complexity coming from an intelligent mind. This means that Christianity's uncaused cause -- God -- is a far better explanation for the origin of our information-rich, meaning-filled universe compared to atheism.
First, in order to recognize an explanation as the best, one needn't have an explanation of the explanation. This is an elementary point concerning inference to the best explanation as practiced in the philosophy of science. If archaeologists digging in the earth were to discover things looking like arrowheads and hatchet heads and pottery shards, they would be justified in inferring that these artifacts are not the chance result of sedimentation and metamorphosis, but products of some unknown group of people, even though they had no explanation of who these people were or where they came from. Similarly, if astronauts were to come upon a pile of machinery on the back side of the moon, they would be justified in inferring that it was the product of intelligent, extra-terrestrial agents, even if they had no idea whatsoever who these extra-terrestrial agents were or how they got there. In order to recognize an explanation as the best, one needn't be able to explain the explanation. In fact, so requiring would lead to an infinite regress of explanations, so that nothing could ever be explained and science would be destroyed. So in the case at hand, in order to recognize that intelligent design is the best explanation of the appearance of design in the universe, one needn't be able to explain the designer.