Power-Domain Non-Orthogonal Multiple Access (PD-NOMA) and index coding have garnered significant attention for their abilities of supporting large-scale mobile connections and reducing network traffic. This paper considers a downlink PD-NOMA wireless network with caching capabilities. We investigate how to minimize transmission delay on PD-NOMA networks with index coding for downlink transmissions. Considering the contents cached by users, we formulate a joint index coding and packet scheduling problem to minimize delay by fully leveraging the characteristics of PD-NOMA and content caching simultaneously. Then, our original proof demonstrates that the problem of delay minimization for downlink PD-NOMA transmission is NP-complete. A two-stage heuristic algorithm is thus set up to solve the problem. In the first stage, a graph is constructed to describe the requirement-caching relationship of users, and the minimum number of packets can be approximated by the clique covering number of the graph. Additionally, for each clique, an index coding packet is formed by XOR requirement packets corresponding to that clique. In the second stage, the index coding packets are scheduled using a heuristic policy that greedily leverages the capabilities of PD-NOMA downlink transmission. Analysis based on simulation results demonstrates that, compared to several baseline schemes, the proposed method effectively reduces transmission delay in cache-aided wireless networks.