Little is known about the evolutionary origins of metabolism. However, key biochemical reactions of glycolysis and the pentose phosphate pathway (PPP), ancient metabolic pathways central to the metabolic network, have non-enzymatic pendants that occur in a prebiotically plausible reaction milieu reconstituted to contain Archean sediment metal components. These non-enzymatic reactions could have given rise to the origin of glycolysis and the PPP during early evolution. Using nuclear magnetic resonance spectroscopy and high-content metabolomics that allowed us to measure several thousand reaction mixtures, we experimentally address the chemical logic of a metabolism-like network constituted from these non-enzymatic reactions. Fe(II), the dominant transition metal component of Archean oceanic sediments, has binding affinity toward metabolic sugar phosphates and drives metabolism-like reactivity acting as both catalyst and cosubstrate. Iron and pH dependencies determine a metabolism-like network topology and comediate reaction rates over several orders of magnitude so that the network adopts conditional activity. Alkaline pH triggered the activity of the non-enzymatic PPP pendant, whereas gentle acidic or neutral conditions favored non-enzymatic glycolytic reactions. Fe(II)-sensitive glycolytic and PPP-like reactions thus form a chemical network mimicking structural features of extant carbon metabolism, including topology, pH dependency, and conditional reactivity. Chemical networks that obtain structure and catalysis on the basis of transition metals found in Archean sediments are hence plausible direct precursors of cellular metabolic networks.