Sensory processing, along with the integration of external inputs into stable representations of the environment, is integral to social cognitive functioning; challenges in these processes have been reported in Autism Spectrum Disorder (ASD) since the earliest descriptions of autism. Recently, neuroplasticity-based targeted cognitive training (TCT) has shown promise as an approach to improve functional impairments in clinical patients. However, few computerized and adaptive brain-based programs have been trialed in ASD. For individuals with sensory processing sensitivities (SPS), the inclusion of some auditory components in TCT protocols may be aversive. Thus, with the goal of developing a web-based, remotely accessible intervention that incorporates SPS concerns in the auditory domain, we assessed auditory SPS in autistic adolescents and young adults (N = 25) who started a novel, computerized auditory-based TCT program designed to improve working memory and information processing speed and accuracy. We found within-subject gains across the training program and between pre/post-intervention assessments. We also identified auditory, clinical, and cognitive characteristics that are associated with TCT outcomes and program engagement. These initial findings may be used to inform therapeutic decisions about which individuals would more likely engage in and benefit from an auditory-based, computerized TCT program.