Contrary to long-held views, recent evidence indicates that $textit{de novo}$ birth of genes is not only possible, but is surprisingly prevalent: a substantial fraction of eukaryotic genomes are composed of orphan genes, which show no homology with any conserved genes. And a remarkably large proportion of orphan genes likely originated $textit{de novo}$ from non-genic regions. Here, using a parsimonious mathematical model, we investigate the probability and timescale of $textit{de novo}$ gene birth due to spontaneous mutations. We trace how an initially non-genic locus accumulates beneficial mutations to become a gene. We sample across a wide range of biologically feasible distributions of fitness effects (DFE) of mutations, and calculate the conditions conducive to gene birth. We find that in a time frame of millions of years, gene birth is highly likely for a wide range of DFEs. Moreover, when we allow DFEs to fluctuate, which is expected given the long time frame, gene birth in the model becomes practically inevitable. This supports the idea that gene birth is a ubiquitous process, and should occur in a wide variety of organisms. Our results also demonstrate that intergenic regions are not inactive and silent but are more like dynamic storehouses of potential genes.
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