Natural proteins represent numerous but tiny structure/function islands in a vast ocean of possible protein sequences not challenged by biological evolution and are yet to be explored by research. Recent studies have suggested this uncharted sequence space endows a surprisingly high structural propensity but understanding of this phenomenon has been awaiting a systematic high-throughput approach. Here we designed, prepared, and characterized two combinatorial protein libraries consisting of randomized proteins, each 105 residues in length. The first library constructed proteins from the entire canonical alphabet of 20 amino acids. The second library used a subset of only 10 residues (A,S,D,G,L,I,P,T,E,V) that represent a consensus view of plausibly available amino acids through prebiotic chemistry. Based on libraries in silico analyses and bulk protease resistance/solubility screening, we report that both canonical and early proteins have a similar structure content. While the inherent solubility of the early library is higher than that of the canonical library, only the latter can be increased by chaperone supplementation. On the contrary, we hypothesize that the early library solubility and folding is enabled by salts and cofactors in the cell-like milieu where these assays were performed. While the early library proteins are inherently more thermostable, stability of both libraries can be elevated by chaperone activity. Interestingly, their structure content remains unchanged. These observations suggest that chaperones play a more significant role with the fully evolved alphabet. In conclusion, our study shows that compact structure occurrence (i) is (up to 40%) abundant in random sequence space, (ii) independent of the general Hsp60 chaperone system activity, and (iii) is not granted solely by the late and complex amino acid additions.