A non sequitur lurks in the reasoning of both Mill and Dawkins. The theory of continental drift explains certain facts, yet for several decades there was no explanation for continental drift itself, until the discovery of plate tectonics. Life was always there' and be done with it. People and DNA still require an explanation, even if we have no explanation for what created them. If we encounter a mysterious probe in space and determine that it is a product of alien intelligence but never learn anything about the aliens themselves, we can hardly complain that we're left in the same position as before.
Explanation is by nature progressive.
The objections hinge upon a misconstrual of the design and cosmological arguments. No proponent of these arguments asserts that all things need a designer or a cause. Everything that begins to exist has cause of its existence. The universe began to exist. Therefore, the universe has a cause of its existence.