Evidence is data that is more likely on a particular hypothesis than on any competing hypothesis.
I would disagree with this definition. Evidence is any data that raises the probability of a hypothesis, even if that probability still remains very low.
You still haven’t explained how/why you infer a supernatural cause from your indirect evidence as opposed to just a natural but as yet unknown explanation.
If the whole of Nature turns out to require an explanation, then we are forced to posit something beyond Nature. On that topic, I suggest you have a look at Dr. Robert Koons’ article, A New Look at the Cosmological Argument, which highlights the contingency of the cosmos as a whole.
When I say that there is no evidence for the supernatural I mean verifiable, objective, and positive evidence.
The sheer contingency of Nature (as discussed in Koons’ article above) arguably satisfies all of the criteria you listed. The fine-tuning argument is another case in point.
Where is your god now?
(1) Why is the death of a species any more morally scandalous than the death of an individual animal? Individuals have feelings; species don’t. A species is an abstraction.
(2) Wouldn’t the end of the Permian have been the proper time to put forward this argument? Now that was an extinction! (And if it hadn’t happened, we probably wouldn’t be here.)
(3) On the subject of extinctions, I suggest you have a look at this article: Historical bird and terrestrial mammal extinction rates and causes by Dr. Craig Loehle and Willis Eschenbach. Here’s the long and the short of it: (i) the vast majority of species extinctions take place on islands (including Australia), not continents; (ii) most extinctions are caused by introduced predators and diseases; (iii) in any case, the island extinction rate is falling, not rising.
(4) Against the doomsayers, may I propose Torley’s Law of Long-Term Consequences: We should not worry ourselves about catastrophes which are projected to take place more than 100 years from now, because the long-term future is radically unforeseeable, owing to the march of technology. (Think of the Internet. And think of Paul Ehrlich’s book, The Population Bomb, and how wrong that turned out to be.) The article you cite says that 1,000,000 species are at risk, but doesn’t say how many are projected to go extinct within the next 100 years.
(5) To date, only one mammalian species is officially recognized as having gone extinct as a result of global warming, and even that case looks a little iffy.
On the subject of something from nothing, I suggest you have a look at physicist Bruce Albert’s scathing review of Dr. Lawrence Krauss’s book, A Universe from Nothing:
On the Origin of Everything
On the question of whether the universe had a beginning, and whether this beginning requires an explanation, the following article by physicist Aron Wall may be of interest to you:
Did the Universe Begin? V: The Ordinary Second Law
Finally, re Alex Vilenkin’s views of God’s existence, it seems to me that he is still open to Platonism, judging from this interview with Robert Lawrence Kuhn:
Alex Vilenkin - Considering God’s Existence?
In any case, it is fallacious of Vilenkin to argue that the laws of physics alone can generate our cosmos. Laws, being abstractions, are incapable of acting. At the very least, some kind of quantum field is required, as an ultimate substrate which instantiates those laws.
What’s more, the beauty of the laws of nature (which is not something subjective, but rather something objective, which even atheist mathematicians are capable of appreciating) points to the existence of a Mind behind Nature, as Robin Collins argues cogently in section 6 of his online article, Multiverses, Design, and the Beauty of the Laws of Nature.