Wouldn’t a system A that is capable of encoding another complex system B, need to be as complex in order to encode all the information in the result?
It’s like a compression algorithm, you can encode the information, but the complexity level of that information is still there (also the difficulty in compressing the information increases very fast - exponentially or maybe even factorially).
So if the most basic protein sequence requires so many bits of information, wouldn’t anything capable of producing that (in a non-random manner) also require at least that level of information (if not more).
It doesn’t matter what process we call systems A and B.
So it seems if randomness doesn’t solve the problem (because math), then the only conclusion is that there is a fundamental requirement for intentionality.