I find drawing that line creates a deistic false dichotomy. Intelligent Design proponents adopt a mechanistic view of the world where God occasionally drops in like a mechanic to assemble (sometimes irreducibly) complex parts. Atheists are quite happy to argue against such a sloppy form of theism. It is child’s play, especially with the overwhelming evidence for evolution on their side. But they are not cogently arguing against God (classical theism). That they cannot do in my experience. What they critique are 17th century philosophical errors that many modern theists have been infected with. A “natural explanation” simply describes how God normally sustains the world. Divine intervention is just God acting beyond that normal order.
To claim a cause is “purely natural”—meaning it operates without God upholding it—is to assume one can disprove God, refute the cosmological argument, and demonstrate that the regularity of nature and the existence of something rather than nothing requires no cause. Instead, one should “lack belief” in the idea of an independent, un-sustained uncaused nature. Naturalists have no explanation for why nature is regular, why it will persist, why it does exist or why anything continues to exist in this exact instant. “Natural explanations” only exclude God if you restrict Him to the gaps in human knowledge. This is why we often say science is neutral. It just explains stuff and neither includes nor excludes God (methodological not philosophical naturalism). The method works but the ultimate nature of reality is beyond its purview.
The reality is God through nature, not God versus nature. Doubt your doubts. The skepticism you have is trained and learned and it’s not neutral or the unquestionable default position of human thought. Your view of the world is influence heavily by a mechanistic philosophy a few hundred years old. It’s part of a philosophical system that you should question like anything else.
Edited to add: And you give guys like deGrasse Tyson way too much credit. He is good at science (a brilliant communicator and a capable astrophysicist–I watch/listen to star talk sometimes) but an utter hack and clown-show when it comes to serious philosophy which he has disparaged in the past. I think Feser’s line about Richard Dawkings would be appropriate for deGrasse Tyson. He wouldn’t know metaphysics from Metamucil.
Vinnie