This paper introduces a reconfigurable intelligent surface (RIS)-assisted grant-free non-orthogonal multiple access (GF-NOMA) scheme. We propose a joint user equipment (UE) clustering and RIS assignment/alignment approach that ensures the power reception disparity required by the power domain NOMA (PD-NOMA). The proposed approach maximizes the network sum rate by judiciously pairing UE with distinct channel gains and assigning RISs to proper clusters. To alleviate the computational complexity of the joint approach, we decouple UE clustering and RIS assignment/alignment subproblems, which reduces run times 80 times while attaining almost the same performance. Once the proposed approaches acknowledge UEs with the cluster index, UEs are allowed to access corresponding resource blocks (RBs) at any time requiring neither further grant acquisitions from the base station (BS) nor power control as all UEs are requested to transmit at the same power. In addition to passive RISs containing only passive elements and giving an 18% better performance, an active RIS structure that enhances the performance by 37% is also used to overcome the double path loss problem. The numerical results also investigate the impact of UE density, RIS deployment, RIS hardware specifications, and the fairness among the UEs in terms of bit-per-joule energy efficiency.