Musical training is associated with a myriad of neuroplastic changes in the brain, including more robust and efficient neural processing of clean and degraded speech signals at brainstem and cortical levels. These assumptions stem largely from cross-sectional studies between musicians and nonmusicians which cannot address whether training itself is sufficient to induce physiological changes or whether preexisting superiority in auditory function before training predisposes individuals to pursue musical interests and appear to have similar neuroplastic benefits as musicians. Here, we recorded neuroelectric brain activity to clear and noise-degraded speech sounds in individuals without formal music training but who differed in their receptive musical perceptual abilities as assessed objectively via the Profile of Music Perception Skills. We found that listeners with naturally more adept listening skills (“musical sleepers”) had enhanced frequency-following responses to speech that were also more resilient to the detrimental effects of noise, consistent with the increased fidelity of speech encoding and speech-in-noise benefits observed previously in highly trained musicians. Further comparisons between these musical sleepers and actual trained musicians suggested that experience provides an additional boost to the neural encoding and perception of speech. Collectively, our findings suggest that the auditory neuroplasticity of music engagement likely involves a layering of both preexisting (nature) and experience-driven (nurture) factors in complex sound processing. In the absence of formal training, individuals with intrinsically proficient auditory systems can exhibit musician-like auditory function that can be further shaped in an experience-dependent manner.