i can see the logic in your reasoning, but IMO, you have it backwards. In the beginning there was no complexity, only an ability to combine and later to duplicate (but I believe this falls under chemistry).
But combinations and duplication leads to sometimes imperceptable complexities (little accidents which affect the duplication process).
Most of these accidental complexities are discarded (natural selection), but some exhibit an advantage over others and survive the natural tests which it encounters. If something survives because it has an advantage, its genetic information will become fixed in the offspring and a new branch of species is created, each branch continuing the process of duplication, variation, adaptabiity, survival, trillions of times. Remember, if the original parent was itself successful, it would also continue survive and create additional variations, which may give opportunity for additional branches to evolve as well as continuing to exist in its simple form.
The great apes and humans are perfect examples of such emerging complexity and intelligence. We have a common ancestor (probably much more apelike than humans) which branched off into several hominid species. As the apes themselves were successful in survival, their duplication remained stable and the evolution of their DNA became fixed in a general sense. However one branch continued to evolve and eventually became homo sapiens. Thus we can find both species present in nature.
The single great difference is that apes have 24 pairs of chromosomes, while humans have only 23 pairs chromosomes. This is due to the “fusing” of two chromosomes into a single chromosome, creating a complex chromosome, which might well have been the cause for our larger brains, while retaining 96 % of the chromosomes which we share with the apes. The other few percent differences gives us our particular human shape, but there is clearly a “familiarity” with great ape appearance and behavior and human behavior.
The complexity we see in nature and in the universe, is a mixture and/or combination of independently evolved structures. There is no “irreducible complexity”. The greatest problem most humans seem to have is a lack of ability to imagine the sheer size, scope, and time involved in the evolution of the universe and all that is contained therein. But if you can accept that our ancestors, billions of years ago sprang from single celled organisms, you will have made a big step toward recognizing the similarities and infinite variety in which evolution works, all by trial and error, but fixing those varieties which have a survival advantage.