In contemporary times, there has been a notable surge in the exploration of pervasive coverage, high-speed data connectivity, and edge computing as pivotal components of prospective sixth-generation (6G) wireless networks. These services are regarded as key components vital for the expected progression in 6G technology. However, the effective realization of these services is heavily contingent upon the existence of resilient network coverage and telecommunication infrastructure. Regrettably, in remote and secluded areas, this infrastructure is frequently absent, presenting formidable obstacles in the attainment of seamless connectivity, extensive coverage, and optimal computation offloading. Targeting the aforementioned horizon, we propose a millimeter wave (mmWave) enabled non-orthogonal multiple-access (NOMA) based access and edge computing network in which high-altitude platforms (HAPs) provide access and edge computing services to ground user terminals. The mmWave spectrum offers huge bandwidth and NOMA due to its inherent benefits enhances system effective throughput and spectral efficiency in comparison to conventional access schemes. We analyze the performance of the proposed network and aim to minimize the execution delay experienced by users in a NOMA cluster offloading their data to edge computing servers located at the HAPs. For minimizing the execution delay, we devise a dual-layer optimization scheme aiming to minimize the transmission and computation delay by optimizing the transmission power and computational resource allocation. The optimization is performed by using Lagrange multipliers method and then convergence is attained by implementing a sub-gradient approach. Optimal power allocation enhances the data rates which subsequently reduces the transmission delay while the optimal cores assignment greatly reduces the computation delay. Simulation results demonstrate the efficacy of our proposed approach, showing a notable reduction in execution delay.