If the answer to the title question is no, the origin of life is not thereby shown to be a supernatural event. It may be an event whose cause we cannot even discover or draw a conclusion about. Or one whose explanation our methods are certain to miss.
We often hear rhetoric along the lines of “The methods of science can solve the origin of life puzzle!” But science is not a magic wand. We may be seeking information that is irretrievably lost. We may be asking meaningless questions, due to a conflict between our underlying assumptions and reality. More insidiously, we may be satisfied with an answer that meets the demands of an underlying belief system while missing the nature of the reality.
Life fascinates us. Recently, a consortium of research institutions paid $840,000 for two lbs. of meteorite ore in which they hoped to find traces of a crash landing from outer space — one that started life on Earth. Yet, curiously, as a special edition of Astrobiology (2011) admitted, “Biologists have been unable to agree on a definition” of life.”
NASA took the lead by defining life as “a self-sustained chemical system capable of undergoing Darwinian evolution.”* When chemist Harry Lonsdale offered $50,000 in 2011 for the best explanation of the origin of life on Earth, he adopted that definition. As an atheist, he made his ultimate goal clear: “The world will learn that the laws of chemistry and physics, and the principle of evolution by natural selection, are sufficient to explain life’s origin.” But the years have not been kind to NASA’s definition. It identifies only one trait, which may not even be universal. For example, life’s simplest cells often evolve by swapping genes, not through Darwinian evolution.
The definition of life has reached the point where science historian George Dyson tells us, “Life is whatever you define it to be.” Richard Dawkins has suggested it is “anything highly statistically improbable, but in a particular direction.” And at a year 2000 international “What is life?” conference, no two definitions were the same. Biochemist Edward Trifonov noted that there are 123 definitions available and, undeterred, promptly proposed his own: Life is self-reproduction with variations. Which was just as promptly contested. In a 2012 issue of philosophy journal Synth�se, Edouard Machery concluded that “scientists, philosophers, and ethicists should discard the project of defining life.”
Still in the game, astrobiologist Charley Lineweaver proposes a new, non-Darwinian approach to defining life:

Many biologists define life as anything that undergoes Darwinian evolution … We pretend that makes sense, but if you look it makes no sense at all. What is the unit of Darwinian evolution? Is it the gene? Is it the cell? Is it a multicellular organism? Is a city evolving? How about Gaia? Is that a life form?

Similarly, evolutionary biologist Bj�rn �stman asks,

Suppose we go to another planet and find one being there, looking exactly like a human being. Everything we can measure about this being confirms that it is just as much alive as you and me. It eats, moves, heals, replenishes, communicates, feels, defecates. Learning more about this being, though, we find that it has no ancestors, and that it does not age. It does not reproduce, and it is the only such being on the planet. Thus, there is no lineage of descent and no population that can evolve. So this being is then not alive? Of course it is. This definition does not work.

Come to think of it, he wonders, if R2D2 from Star Wars existed, would he be alive?
More provocatively still, in Scientific American, Ferris Jabr ends up concluding that life is just a continuum from non-life and doesn’t really exist as a separate category. If we could see the underlying reality of our planet, we would see

… the innumerable atoms that make up everything on the planet continually congregate and disassemble themselves, creating a ceaselessly shifting kaleidoscope of matter. Some of those flocks of particles would be what we have named mountains, oceans and clouds; others trees, fish and birds.

The trouble is, we know better.
So the first clue about the adventure that we are in for is: Life is a state, an experience, that everyone has and thinks they can recognize in other people and things. A quality we think is very important. Yet no one can define it.
Darwin proposed a mechanism for the evolution of existing life — natural selection acting on random mutation — but, a prudent man, he stopped well short of proposing to account for life’s origin. Some of his followers pressed ahead. They ask us to imagine “self-replicating entities,” protocells, and “prebiotic life” (essentially, pre-life) that somehow evolved their way to life long ago. At New Scientist, Michael Marshall assures us,

Once the first self-replicating entities appeared, natural selection kicked in, favouring any offspring with variations that made them better at replicating themselves. Soon the first simple cells appeared. The rest is prehistory.

It must be prehistory. No such chains, protocells, or pre-life are found in a wild state today. And even the fabled “minimal cell” is more complex than expected.
Some origin-of-life theorists respond by making Darwin’s natural selection into an intelligent agent, the precise opposite of his intention. Stephen J. Freeland of the NASA Astrobiology Institute attributes the fact that “life knew exactly what it was doing” to — natural selection. He tells us, ” … life seemingly did not choose its twenty building blocks randomly.” Indeed, “We found that chance alone would be extremely unlikely to pick a set of amino acids that outperforms life’s choice.”
When materialism governs science, that extreme unlikelihood can mean only one thing: There must be a law.