With the growing applications of the Internet of Things (IoT), a major challenge is to ensure continuous connectivity while providing prioritized access. In dense IoT scenarios, synchronization may be disrupted either by the movement of nodes away from base stations or by the unavailability of reliable Global Navigation Satellite System (GNSS) signals, which can be affected by physical obstructions, multipath fading, or environmental interference, such as such as walls, buildings, moving objects, or electromagnetic noise from surrounding devices. In such contexts, distributed synchronization through Non-Orthogonal Multiple Access (NOMA) offers a promising solution, as it enables simultaneous transmission to multiple users with different power levels, supporting efficient synchronization while minimizing the signaling overhead. Moreover, NOMA also plays a vital role for dynamic priority management in dense and heterogeneous IoT environments. In this article, we proposed a Two-Stage NOMA-Enabled Framework "TSN-IoT" that integrates the mechanisms of conventional Precision Time Protocol (PTP) based synchronization, distributed synchronization and data transmission. The framework is designed as a four-tier architecture that facilitates prioritized data delivery from sensor nodes to the central base station. We demonstrated the performance of "TSN-IoT" through a healthcare use case, where intermittent connectivity and varying data priority levels present key challenges for reliable communication. Synchronization speed and end-to-end delay were evaluated through a series of simulations implemented in Python. Results show that, compared to priority-based Orthogonal Frequency Division Multiple Access (OFDMA), TSN-IoT achieves significantly better performance by offering improved synchronization opportunities and enabling parallel transmissions over the same sub-carrier.