During the origin of life, the biological information of nucleic acid polymers must have increased to encode functional molecules (the RNA world). Ribozymes tend to be compositionally unbiased, as is the vast majority of possible sequence space. However, ribonucleotides vary greatly in synthetic yield, reactivity and degradation rate, and their non-enzymatic polymerization results in compositionally biased sequences. While natural selection could lead to complex sequences, molecules with some activity are required to begin this process. Was the emergence of compositionally diverse sequences a matter of chance, or could prebiotically plausible reactions counter chemical biases to increase the probability of finding a ribozyme? Our in silico simulations using a two-letter alphabet show that template-directed ligation and high concatenation rates counter compositional bias and shift the pool toward longer sequences, permitting greater exploration of sequence space and stable folding. We verified experimentally that unbiased DNA sequences are more efficient templates for ligation, thus increasing the compositional diversity of the pool. Our work suggests that prebiotically plausible chemical mechanisms of nucleic acid polymerization and ligation could predispose toward a diverse pool of longer, potentially structured molecules. Such mechanisms could have set the stage for the appearance of functional activity very early in the emergence of life.