Information can evolve as a physical consequence of non-equilibrium dynamics, even in the absence of genes, replication, or predefined fitness functions. We present Stability-Driven Assembly (SDA), a framework in which stochastic assembly combined with differential persistence biases populations toward longer-lived motifs. Assemblies that persist longer become more frequent and are therefore more likely to participate in subsequent interactions, generating feedback that reshapes the population distribution and implements fitness-proportional sampling, realizing evolution as a natural, emergent genetic algorithm (SDA/GA) driven solely by stability. We apply SDA/GA to chemical symbol space using SMILES fragments with recombination, mutation, and a heuristic stability function. Simulations show hallmark features of evolutionary search, including scaffold-level dominance, sustained novelty, and entropy reduction, yielding open-ended dynamics absent from equilibrium models with fixed transition rates. These results motivate an evolutionary ladder hypothesis where persistence-driven selection precedes genetic replication.

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