A typical protein contains about about 300 amino acids. The probability of building a 150-amino-acid-length chain at random in which all bonds are peptide bonds and all amino acids are L-form (functioning proteins tolerate only left-handed amino acids) is roughly 1 chance in 10^180.
To put this in perspective, the chance of winning the Mega Millions lottery is about 10^8.
And 10^180 is just for one simple protein. A complete bacterium is composed of hundreds or thousands of enzymes & proteins.
Yes, amino acids are simple for nature to build randomly, and yes, proteins are insanely complex and their random formation is incredibly against the odds - but, you know, odds are anything that is possible, regardless of statistical probability, becomes more likely the more time you put into the equation.
Millions and billions of years = holy shit.
We insignificant little humans have not even been around for half a million years, at most (best estimates for our exact species are about 250k years iirc)... human civilization with actual governance and all the fun that comes with empires like early tribal human sacrifices and the discovery of OMG these drugs are awesome.... has only been around for no more than 10,000 years iirc.
Now put that into perspective, and try to imagine how many years are actually in a billion years. I'll give you a hint, I just said it.
Smart humans (civilization) have been around for approx. 0.00001 billion years. Multi-celled organisms have been around for approx 0.6 billion years.
...
Ah, screw it. Look at
this picture, it gives a far better representation of life and time.
Before the first single-celled creature, there was a ton of time where all that was happening on Earth can be summed up as, well... hell.
All it was doing was spewing up toxic fun all over the place, probably raining acid, not much water but likely a ton of tasty molten rock.
Oh, and let's not forget, Earth was an epic whore, taking money shot after money shot from galactic travelers, letting all sorts of shit rain down. And then, one day, there was one hell of a visitor, a planetoid of some sort, knocked up Earth something fierce - a long, long period of morning sickness meant an epic amount of our guts were spewed into space, and before we knew it... Earth had a new baby Moon.
Organic material, and even life, could have popped up during Earth's worst days, we don't know it. We know the probability of it all happening, but we don't know how many times it actually happened on Earth - quite a few times of epic hell kind of meant anything actually alive would cease to exist. Our most sound guess currently: it happened at least once, and possibly only once. Of course, that was enough, you see.
But for over a billion years, there was absolutely nothing on Earth, well, at least nothing that the Earth feels must be shared with us humans. The bitch has her secrets, and probably doesn't care to share them with that nasty rash of the bipedal plague that feeds on her now.
There is one theory that you might enjoy:
Some alien species shot their glorious seed, or some vile concoction, all over Earth. And here we are now.