Latency-constrained aspects of cellular Internet of Things (IoT) applications rely on Ultra-Reliable and Low Latency Communications (URLLC) which highlight research on satisfying strict deadlines. In this study, we address the problem of latency constrained communications with strict deadlines under average power constraint using Hybrid Multiple Access (MA) which consists of both Orthogonal MA (OMA) and power domain Non-Orthogonal MA (NOMA) as transmission scheme options. We aim to maximize the timely throughput, which represents the average number of successfully transmitted packets before deadline expiration, where expired packets still waiting in the buffer are dropped. We use Lyapunov stochastic optimization methods to develop a dynamic power assignment algorithm for minimizing the packet drop rate while satisfying time average power constraints. Numerical results show that Hybrid MA improves the timely throughput compared to conventional OMA by up to 46% and on the average by more than 21% while satisfying average power constraints.