The emergence of the first polymers played an essential role in the transition from the physicochemical to the biological domain, a perception that embodied many different world paradigms relying on only one primal polymer. However, biological complexity would have appeared with an increasing set of associated chemistries and molecular interactions of many different macromolecules. In agreement with this notion, here, the purpose is to focus specific attention on current knowledge of modern biochemistry of a set of widespread polymers likely present in the Last Universal Common Ancestor synthesized by nontemplate-driven reactions with references to their abiotic synthesis. The proposed overview describes the manner in which these polymers could have organized around two polymerization reaction cycles and integrated into a minimal organizational closure at the early stages of living systems, independently of template replication processes. This hypothesis could provide an alternative conceptual framework to evaluate a plausible scenario addressing the transition from nonliving to protocellular systems.