In this paper, we investigate an uplink communication scenario in which multiple users communicate with an access point (AP) employing non-orthogonal multiple access (NOMA). A pinching antenna, which can be activated at an arbitrary point along a dielectric waveguide, is deployed at the AP to dynamically reconfigure user channels. The objective is to maximize the system sum rate by jointly optimizing the pinching-antenna's position and the users' transmit powers. The formulated optimization problem is non-convex, and addressed using the particle swarm optimization (PSO) algorithm. For performance benchmarking, two time division multiple access (TDMA) schemes are considered: one based on the pinching antenna individually activated for each user, and the other based on the single-pinching-antenna configuration serving all users. Numerical results demonstrate that the use of the pinching antenna significantly enhances the system sum rate compared to conventional antenna architectures. Moreover, the NOMA-based scheme outperforms the TDMA-based scheme with a single pinching antenna but is outperformed by the TDMA-based approach when the pinching antenna is adaptively configured for each user. Finally, the proposed PSO-based method is shown to achieve near-optimal performance for both NOMA and TDMA with a common pinching-antenna configuration.