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Going from a short segment of DNA randomly popping into existence, capable of nothing but self-replication to living organisms, carrying a tremendous amount of intelligence, those are two very different things.

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.

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Once the process is started with simple life evolution just causes complexity as a rule. I think people who can't believe evolution made us from "nothing" have never really tried to understand the time frame in which it happend, which is a really long time.

Humans can't conceive of large timescales nor large numbers. That's why I use my Rubik's Cube example. A single glass of water contains enough molecules that if they were each a random Rubik's cube then there's a mathematical certainty that 512 of them will be perfectly solved (per glass).

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.

But this is more of a proof how insanely big a mole is, rather than the fundamental question. Also, Rubik’s cube possibilities is not that high. Try to create each permutation of a standard deck of cards (hint: there are less atoms in the universe than the number of permutations)

About the 'card deck' combinations: That's why we can be virtually certain there are no life forms in the universe that consist of a chain molecule (as it's version of "DNA") where there's more than a handful of different types of molecules along the chain.

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)

Life is not built on ‘binary’, there are 4 bits. All four nucleotides take part in the encoding (reading happens on one thread only).

And since life was presumably started with RNA, we are still talking about 4 base elems

It's perfectly legitimate to say life stores information using only two "types" of things (AT or GC) which can be oriented one way or another, which is a "binary choice of the type". I explain it that way because it reaches a wider audience (easier to visualize)

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!!

I did think about that, that’s why I added the second paragraph, namely that what about RNAs? (Since presumably they precede the DNA world) They can self-bind (I don’t know the proper nomenclature in English), but by all means they have 4 bases.