The Problem of Causation in the Argument from Design

Can we know whether the creation of the universe was a result of mere chance or whether it was created by God? Eighteenth century British philosopher David Hume argued that little can be known about the cause of the universe. Hume's critique of the notion that we can know the cause of the creation of the universe is based on "the argument from design." The argument from design holds that the universe is similar to a fine-tuned machine in that it is extremely complex, yet efficient. A fine-tuned, complex machine has a designer; therefore, it is reasonable to think that the universe has a designer too. Supporters of this view have assigned God as the designer of the universe; therefore God can be thought of as the "cause" of the universe.
Hume develops three responses to the argument from design. The problem of causation in the argument from design is what will be explored here. The problem of causation raises the question of what can be known about a cause of something, based on evidence of a single effect, especially when the effect is like nothing else ever experienced previously.
To begin, Hume argues we can only know the causal relation between a cause and its effect by a constant conjunction between the two events. We cannot infer the cause of an effect unless we have experience of these events being constantly conjoined. For example, we know that bringing a pot of water to a temperature of 100 degrees Celsius causes the water to boil. We know this because every time we boil water, it always starts boiling when it reaches 100 degrees Celsius. Thus, there is a constant conjunction between this specific temperature and the point at which water boils. However, with the case of the creation of the universe, we have no experience of a constant conjunction between God (the cause), and the creation of our universe (the effect), because the creation of our world is a one-time event; it is unlike any other event we have experience of. Therefore, as Hume would argue, we cannot infer anything about the cause of this effect, because we have no experience of a constant conjunction between the two events (i.e. between God - the cause, and our world - the effect).
I think Hume's argument effectively rejects the conclusion drawn from the argument from design. The argument from design concludes that the universe is designed. If it is true that the universe has a designer, it is fair to call this designer the cause of the universe. However, Hume's argument rejects the notion that we can know the cause of some effect based on only a single occurrence of that event. Therefore, we cannot infer that the cause of the universe is some designer. Perhaps the cause of the universe is something entirely different than a designer; maybe the universe is the result of mere chance. Setting aside scientific evidence and spiritual beliefs about the creation of the universe, the point Hume is making is that it is only after experience of constant conjunction between cause and effect that we can come to know the cause of a given effect. The creation of the universe however, has only occurred once, hence, there is no experience of constant conjunction; therefore we cannot infer the cause of the universe. The creation of the universe is unlike any other effect we have experience of; it is unique. Therefore we have no adequate examples of cause and effect to compare it to. Any analogy meant to draw a comparison between itself and the creation of the universe must fall short for this reason. Yet the very basis of the argument from design rests on analogy alone.
One criticism that might be raised against Hume's argument is that he presupposes that the world is an effect. If it could somehow be shown that universe is not an effect, Hume's argument would no longer have any force, because his argument rests entirely on the idea of the relation between cause and effect.