A common style of religious argument is the "God of the gaps". These types of arguments basically point at an area of incomplete knowledge, and insert God as an explanation. Some of the common ones focus upon the origin of life on Earth, the origin of the universe, and the origin of human consciousness. All of these can be responded to in the same way.
First off, the logic is junky. What these arguments are doing is pointing out that science lacks an explanation for something, and then saying "therefore, we can conclude that my explanation is correct." This makes absolutely no logical sense. It's like saying "We don't know who committed the murder. Therefore, Steve committed the murder." The only thing that a lack of an explanation is evidence for is a lack of an explanation.
Another thing to point out is that science might one day provide an explanation for these things, even if it can't currently. In fact, precisely this has happened to a number of things that people previously thought had supernatural explanations: disease, natural disasters, storms, thunder and lightning, crop failure, the points of light in the night sky—all of these things were thought to be manifestations of the supernatural by our ignorant ancestors. We now have scientific explanations for these things, and we understand how ridiculous and illogical it was for people in the past to jump to the conclusion that the gods were responsible.
This is exactly the position that modern day creationists are in when they make God of the gaps arguments. Logically, they're on equal footing with the fools of the past who thought that thunder was best explained by the gods.
As Neil DeGrasse Tyson once said, "If that's how you want to invoke evidence for God, then God is an ever-receding pocket of scientific ignorance." Once we explain the origin of life, the universe, and consciousness scientifically, where will God be left to hide?
The rational response to ignorance is an honest acknowledgement that we don't yet know the answer. When faced with this realization, the correct course of action is to further investigate and work harder to discover the answer—not conclude that the explanation is a supernatural phenomenon and cease all further inquiry.