From something much simpler, and which has been iterating for approx 4 billion years.
Here's my best analogy: If you take one mole of "random" Rubik's Cubes (the number of molecules in a glass of water), then search for 'Solved' ones you'll find 512 are magically solved, merely by the power of large numbers. The ways molecules can 'snap together' are similarly 'finite', just like a puzzle.
Now think how many glasses of water are on earth. A replicating molecule would have existed probably on the FIRST DAY earth had cooled enough to form water.
If we knew what the shortest sequence if DNA is that can replicate, we'd be able to mathematically state the probability of it existing in any 'random' length of DNA of that length as 1/(4^N) where N is DNA length (number of AT/GC pairs).
Take it as 200 bases and you won't find another life in the observable universe. Avogadro's number is no match for exponential growth.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3943892/
"The present study describes the directed evolution of replicating RNA enzymes that operate with an exponential growth rate of 0.14 min−1, corresponding to a doubling time of 5 min. Each parental enzyme can give rise to thousands of copies per hour, and each of these copies in turn can do the same, all the while transmitting molecular information across the generations."
According to my math 10 million moles of random sequence 50-base pair RNA segments would be required to ensure a correct 'Hit' on a replicator, assuming only one of those 50-long sequences can replicate. 4^50=10^30. 10^30/Avogadro=10^7. Assuming each enzyme is the size of a water molecule, that would be about one large swimming pool of water.
In actual evolution this number of RNA molecules can be thought of as 'diluted' across the entire oceans, and not magically sitting in single pond.
But do you? If elements A and B tend to form compound A-B, and compound A-B can attach a further set of A and B, forming B-A-B-A which under certain circumstances will split into A-B and A-B, you have basic reproduction, and perhaps the occasional presence of element C will expedite the process. Game of life. In my [very] layman's view of the world, given a billion years or two, some such infinitely simple process should be enough to get the ball rolling, as long as it can somehow produce an ever so slightly errorprone copy.
To make an analogy, what you describe would be only the electronic chips or the logic gates of a computer. There are a still the CPU, RAM, and the whole software stack from the OS that runs our bodies (and mind you, there is a different one for each species) to the yet unknown abstractions from which human general intelligence emerges.
I think people underestimate how difficult it is for all the above to get started by accident.
For molecules that are a linear chain of only 2 possible items in the chain, it becomes a 'brute force search' of a 'puzzle space' to find a chain that 'does something like computer code', and the earth has the computing power to solve that brute force problem in 30 seconds, not 30 million years.
Nature is statistically guaranteed to find the simplest patterns first and that's why our life is built on 'binary' (two kinds of 'cards' AT/GC). Life on all planets will likely use binary "information storage", especially because of it's modularity (i.e. it can be cut-n-pasted together in different patterns)
And since life was presumably started with RNA, we are still talking about 4 base elems
However there's always at least one stickler who wants to quibble that the orientation is also a "binary bit" of information. Congratulations, you're him today!!
A code with a 4 letter alphabet would be 2 letter, if it happened to use a parity “bit” or other error correction info?
However there may be slightly more requirements like the sequence has to be found in an oil film (bubble) up until it can form a skin/membrane, to protect itself, so even if it was happening on earth trillions of times every day no one would be there to discover it, and other life on the planet with a head start (bacteria, etc) would consume it before it made more 'progress' by evolution.
In the early planet there was nothing to "eat up" life as it was starting. Everything was on an equal footing.
For example, if I understand this correctly, a random jumble of DNA as you describe would have a 50/50 chance of twisting to the right or twisting to the left. And yet all life on earth uses DNA that is "right handed" twisting to the right.
It's already experimentally proven you can mix up N, H, and O and it spontaneously forms RNA. We've even found entire RNA and sugars on meteorites. It's not rare in nature, it's abundant and self-emergent from the raw atoms themselves.
Now, either there were some naturally formed impermeable areas with an abundance of base material (yet again, I’m not saying life emerged because the UFOs created it), or we are talking about many orders of magnitude less statistical chances. I am willing to believe that many, not individually extraordinary thing had to happen at the same time, that made life possible - but that pretty much makes their combined presence extraordinary, which is my claim.
(Some form of underwater volcanic caves or whatever could sound like a possibility, especially because last I checked, starting sticked to a surface with certain catalytic activities is a plausible theory. Especially due to the reduced statistical chances due to a 2D surface instead of a 3D one! What I have a bit of trouble seeing, is how did organic materials form - I am aware of the famous experiment with lightning bolts that created ammonia and some other chemicals, but it would only slowly increase their uniform distribution in the oceans. Perhaps some chemical reaction with gases that made them accumulate? )
That's well known. It is the key driver for the global contraceptives market, which generated revenue of $28,175 million in 2015 and is estimated to reach $43,812 million by 2022.
We are familiar with downs syndrome, 3 rather than the intended 2 copies of chromosome 21, only because it's comparatively viable.