De novo emergence, and emergence of the earliest proteins specifically, demands a transition from disordered polypeptides into structured proteins with well-defined functions. However, can peptides confer evolutionary relevant functions, let alone with minimal abiotic amino acid alphabets? How can such polypeptides evolve into mature proteins? Specifically, while nucleic acids binding is presumed a primordial function, it demands basic amino acids that do not readily form abiotically. To address these questions, we describe an experimentally-validated trajectory from a phase-separating polypeptide to a dsDNA-binding protein. The intermediates comprise sequenceduplicated, functional proteins made of only 10 amino acid types, with ornithine, which can form abiotically, as the only basic amino acid. Statistical, chemical modification of ornithine sidechains to arginine promoted structure and function. The function concomitantly evolved -from phase separation with RNA (coacervates) to avid and specific dsDNA binding -thereby demonstrating a smooth, gradual peptide-to-protein transition with respect to sequence, structure, and function.