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This paper investigates the benefits of integrating multiple reconfigurable intelligent surfaces (RISs) in enhancing the timeliness performance of uplink Internet-of-Things (IoT) network, where IoT devices (IoTDs) upload their time-stamped status update information to a base station (BS) using non-orthogonal multiple access (NOMA). Accounting to the potential unreliable wireless channels due to the impurities of the propagation environments, such as deep fading, blockages, etc., multiple RISs are deployed in the considered IoT network to mitigate the propagation-induced impairments, to enhance the quality of the wireless links, and to ensure that the required freshness of information is achieved. In this setup, an optimization problem has been formulated to minimize the average sum Age of Information (AoI) by optimizing the transmit power of the IoTDs, the IoTDs clustering policy, and the RISs configurations. The formulated problem ends up to be a mixed-integer non-convex problem. In order to tackle this challenge, the RISs configurations are first obtained by adopting a semi-definite relaxation (SDR) approach. Then, the joint power allocation and user-clustering problem is solved using the concept of bi-level optimization, where the original problem is decomposed into an outer IoTDs clustering problem and an inner power allocation problem. Optimal closed-form expressions are derived for the inner problem and the Hungarian method is invoked to solve the outer problem. Numerical results demonstrate that our proposed approach achieves lowest AoI compared to the other baseline approaches.