In short: Within the fundamental model of societal growth, does socialism only follow after capitalism, or is socialism philosophically capable of standing alone as a principle ideology during the consutruction of a society?
Long form: In a hypothetical pre-society, 3-5 people of the same plot of land equipped with only the knowledge of sticks and stones, band together to mark the initiation of a society with the goal to reproduce and explore/innovate within science, geography, literature, economics, manufacturing, ect., to establish an infrastructure of societal growth that would be fundamental to the underlying success of the advanced society their progeny find themselves playing video games in. For simplicity, let's say the growth/advancement of the society followed a sigmoidal trend over 1000 years, where extreme growth was preceded and succeeded by a relative plateau:
During societal development, would centralized socialism ever be favored to secure equality of outcome for each individual, at the expense of progress (natural selection by societal contribution) and available utilities (individual cost/benefit of food, water, attention, ect.)?
Or, would capitalism, as a vehicle for 'natural selection by societal contribution', inherently be required for societal establishment up until the second plateauing of the society's growth, in which only then higher degrees of socialism could be implemented?
Revised: (at the request to narrow the scope)
Can socialism be a principle ideology during the growth of society; or does capitalism always precede socialism?
*socialism def: individuals and businesses own the means of production, socialize the profits to ensure principled outcome equality of citizens.
*societal growth def: In the context of endogenous growth theory; growth curve is positively sigmoidal in the example indicating non-sustainability of high-growth phase.
*note: I understand my question may solicit some opinion; though I do not see any material addressing this question anywhere on the web (perhaps I'm missing it); so I do apologize as I cannot guarantee succinct factual answers despite the potential validity of the question.