We propose and evaluate the performance of a Non-Orthogonal Multiple Access (NOMA) dual-hop multiple relay (MR) network from an information freshness perspective using the Age of Information (AoI) metric. More specifically, we consider an age dependent (AD) policy, named as AD-NOMA- MR, in which users only transmit, with a given probability, after they reach a certain age threshold. The packets sent by the users are potentially received by the relays, and then forwarded to a common sink in a NOMA fashion by randomly selecting one of the available power levels, and multiple packets are received if all selected levels are unique. We derive analytical expressions for the average AoI of AD-NOMA-MR. Through numerical and simulation results, we show that the proposed policy can improve the average AoI up to 76.6% when compared to a previously proposed AD Orthogonal Multiple Access MR policy.