Maximum completion time is a key performance metric for future wireless applications that have stringent latency requirements. This letter studies its optimization in uplink multisubcarrier non-orthogonal multiple access (NOMA) networks. The joint optimization problem of power allocation, user pairing and scheduling is analyzed and proved to be NP-hard. To tackle the problem, the power allocation subproblem for a single NOMA pair is first derived. Next, for the joint user pairing and scheduling subproblem, an optimal algorithm for a special case is constructed and a suboptimal algorithm for the general case is designed. Our proposed scheme is applicable to data aggregation in wireless federated learning networks, and simulation results validate its superior performance.