The noncoding genome plays an important role in de novo gene birth and in the emergence of genetic novelty. Nevertheless, how noncoding sequences’ properties could promote the birth of novel genes and shape the evolution and the structural diversity of proteins remains unclear. Therefore, by combining different bioinformatic approaches, we characterized the fold potential diversity of the amino acid sequences encoded by all intergenic open reading frames (ORFs) of S. cerevisiae with the aim of (1) exploring whether the structural states’ diversity of proteomes is already present in noncoding sequences, and (2) estimating the potential of the noncoding genome to produce novel protein bricks that could either give rise to novel genes or be integrated into pre-existing proteins, thus participating in protein structure diversity and evolution. We showed that amino acid sequences encoded by most yeast intergenic ORFs contain the elementary building blocks of protein structures. Moreover, they encompass the large structural state diversity of canonical proteins, with the majority predicted as foldable. Then, we investigated the early stages of de novo gene birth by reconstructing the ancestral sequences of 70 yeast de novo genes and characterized the sequence and structural properties of intergenic ORFs with a strong translation signal. This enabled us to highlight sequence and structural factors determining de novo gene emergence. Finally, we showed a strong correlation between the fold potential of de novo proteins and one of their ancestral amino acid sequences, reflecting the relationship between the noncoding genome and the protein structure universe.