The paper explores the joint optimization of beamforming and phase shifts in Intelligent Reflecting Surface (IRS)-aided Non-Orthogonal Multiple Access (NOMA) systems within the context of 6G networks. We propose a novel algorithm that optimizes the beamforming vectors at the base station (BS) and the phase shifts at the IRS to maximize the sum rate of the system. Our approach leverages alternating optimization and successive convex approximation methods to tackle the non-convex nature of the problem. Extensive simulations demonstrate that the proposed method significantly exceed conventional schemes, achieving up to 30% improvement in spectral efficiency. These results underline the potential of IRS-NOMA integration in the fulfillment of ambitious 6G performance targets. The conclusions of this study contribute to the development of more efficient and reliable wireless communication systems that prepare a journey for the next generation of mobile networks.