The odds of self aware consciousness arising in any randomly selected universe is (let's say for argument sake) 1 in a trillion.
Two things here:
1) No one, least of all scientists, is proposing that a self-aware consciousness arose by a feat of random chance, like a monkey banging on a piano just happening to play a perfect Mozart concerto.
2) If the odds of ordinary self aware consciousness arising in a randomly selected universe is 1 in a trillion, what are the odds of an omniscient, omnipotent, infinitely complex
self-aware consciousness just happening somewhere? 1.
Richard Dawkins has a wonderful analogy for the evolutionary process: "Climbing Mt. Improbable." Imagine you're standing at the base of an enormous, sheer cliff. No matter how hard you try, you can't leap up there, and there are no handholds. So you decide that only a God, or maybe a superhero could ever hope to reach the summit of Mt. Improbable. In like manner, the idea of a self aware intelligence, or even a fully-developed eukaryotic cell just falling together by random chance is such a high improbability cliff that it cannot be scaled.
But if, instead of trying to leap to the top in one go, you walk around the back, you'll find that behind the cliff there's a long, gentle slope you can walk up easily. Thus, without any divine magic or super powers, or even any mountain-climbing skills, you can walk right up to the top of Mt. Improbable. In like manner, through a long process of evolution by natural selection, small, slightly-improbable steps (mutations) that "work" (at the job of perpetuating themselves) are able to survive, reproduce, and repeat the process with the next step until the Mt. Improbable of self aware intelligence is reached. It doesn't even take a full-blown modern cell to start, just a kludge of chemicals inside a lipid bubble (like what you see if you try to mix oil with water) in an environment where the chemicals can start an autocatalytic reaction. As soon as you've got something surviving and reproducing, the non-random
ratchet of natural selection kicks in, and evolution is off to the races.2.
Any god or goddess is far more complex--and thus more improbable--than the first protocell, the Boeing 747 made by a tornado sweeping through a junkyard, or the most amazing human being who ever lived. So, before you start hunting the speck of improbability in our world view, better get the plank of improbability out of yours first.
Now how many universes do we know of ? Just one. Not millions of universes till we get the right one. Not lots of picks from the deck. No, just one universe. Just one pick from 20 billion decks of cards.
But we don't know there's just one Cosmos, either. One of the multiverse cosmologies could be right. Furthermore, virtually all of this Cosmos is
barren of life. Earth is statistical noise. But let's take your one in a trillion odds. There's about 100 billion to 400 billion stars in the Milky Way. Let's take the lower number. There's about 100 billion galaxies of comparable size (some smaller, some larger) within the extent of the Cosmos that we can see. There could be more over the Cosmic horizon.
There is some evidence that objects that we can see are being gravitationally pulled toward objects we can't see. The unseen objects would be within the Cosmic horizon of the objects they're attracting, but not ours, since we are further away. This is called "Dark Flow."
So, I think we would have a solid basis for thinking that the Cosmos is bigger than what we can see, but let's take the conservative figure of 100 billion galaxies. 100 billion galaxies x 100 billion stars in each = 10,000 billion, or 10 trillion chances for life. Given your proposed one in a trillion probability, this means the "ace" of life is going to come up about ten times. And this doesn't count multiple tries per star, when it probably should. Each star has multiple planets and moons, and a Cosmic age of about 14 billion years. Life on Earth started about 3.8 billion years ago, not too long after the meteors stopped falling and the surface solidified. Such a quick start could imply the odds aren't nearly as bad as 1 in a trillion. Since there are solar systems far older than ours, life in those systems would have had even longer to "get lucky" and start evolving.
Furthermore, we've discovered fairly recently that life can survive in surprisingly harsh environments. Bacteria and little critters called water bears can even survive in the vacuum of space. So, life may not even require an Earth-like world to get started, which could give it many more chances. At any rate, even with your exaggerated probability number, we would expect at least ten planets with self aware intelligent life emerging randomly. And guess what: we are one!
"So what!" say the skeptics. "What's so special about this universe anyway ? What's so special about life, about consciousness, about order ?"
Answer: If this universe is not special then a combine harvester coming together by chance is not special.
The Boeing 747 (or Combine) Argument bites you harder than it bites us, since you have to explain how an infinitely complex
superduperbeing "just happened to exist." All we need is some chain molecules in a bubble of fat.
Tautology. Only in a universe where intelligent consciousness arises can we even discuss these questions.
Answer: But it is the only universe that we know of. The combine harvester (an analogy for life and intelligent consciousness) has come together by chance in the only universe that we know of.
Combine harvesters don't reproduce, and they don't have ancestors. That means evolution by natural selection doesn't apply to them as it does to living beings.
If watches could but tiny watchlings breed,
Their offspring on minutest clocksprings feed,
And win their loves by telling truest time,
Of watchmakers then, we would have no need.
There may be many universes. Infinite in fact. All with different conditions.
Answer: Unscientific. Untestable. Unobservable. As much a matter of faith as any religion.
If stated as a certainty without any evidence, yes. But then, as I've already shown, this Cosmos is big enough. You have to move the goalposts by an order of magnitude before we're even down to a probability of 1 in 1 for life to emerge randomly. And again: no matter how much you move the goalposts, they move further for you, because you're asserting that an infinitely complex
form of self aware life "just happens to exist."
We, at least, have a theory (evolution by natural selection) supported by literal mountains of evidence, that shows us how to climb to the top of Mt. Improbable. You have no explanation at all
for the emergence of self aware life, except to posit an infinite amount of it somewhere else. You can't plug a hole in understanding with an infinitely larger hole.