Occasionally, new protein-coding genes arise de novo from noncoding DNA and not from duplication and divergence of other genes. De novo originating proteins will be restricted to the taxa that persist following the emergence of the new protein-coding gene: older de novo protein-coding genes will have homologs in more distantly related taxa whereas younger de novo protein-coding genes may be restricted to few closely related taxa. The historical progression of de novo protein-coding genes---from noncoding sequence to presence in a single species to presence in multiple taxa---has led to the theory that proteins should fall along a "continuum" where the traits of the youngest proteins should more closely resemble those of noncoding sequence than those of older proteins, as would be expected if protein-coding genes emerged entirely by chance. An alternative “preadaptation” theory predicts that the youngest proteins will have extreme gene-like trait values because selection will remove all toxic noncoding sequences, which never go on to persist as protein-coding genes. These trait values may even be more exaggerated in younger proteins than in older proteins that have had more time to evolve subtle solutions to structural constraints. We examined intrinsic structural disorder (ISD) as a trait with the potential to distinguish between the competing theories. We inferred ISD from the sequences of all mouse proteins and paired intergenic noncoding sequences after assigning evolutionary ages to each mouse protein via homology-based phylostratigraphy. We found that younger proteins have a higher intrinsic structural disorder (ISD) than older proteins, and proteins translated from intergenic noncoding sequences have the lowest ISD, contradicting the continuum theory of de novo gene birth and confirming the alternative theory of preadaptation. Our results are robust to homology detection bias (i.e. to evolutionary rate as a confounding factor), to non-genes erroneously annotated as species-specific proteins, and to correcting the flawed but common practice of exaggerating statistical significance by treating genes, rather than gene families, as independent data points.