In cases of severe wildlife population decline, a key question is whether recovery efforts will be impeded by genetic factors, such as inbreeding depression. Decades of excess mortality from gillnet fishing have driven Mexico's vaquita porpoise (Phocoena sinus) to ~10 remaining individuals. We analyzed whole-genome sequences from 20 vaquitas and integrated genomic and demographic information into stochastic, individual-based simulations to quantify the species' recovery potential. Our analysis suggests that the vaquita's historical rarity has resulted in a low burden of segregating deleterious variation, reducing the risk of inbreeding depression. Similarly, genome-informed simulations suggest that the vaquita can recover if bycatch mortality is immediately halted. This study provides hope for vaquitas and other naturally rare endangered species and highlights the utility of genomics in predicting extinction risk.