The recent interweaving of AI-6G technologies has sparked extensive research interest in further enhancing reliable and timely communications. \emph{Age of Information} (AoI), as a novel and integrated metric implying the intricate trade-offs among reliability, latency, and update frequency, has been well-researched since its conception. This paper contributes new results in this area by employing a Deep Reinforcement Learning (DRL) approach to intelligently decide how to allocate power resources and when to retransmit in a \emph{freshness-sensitive} downlink multi-user Hybrid Automatic Repeat reQuest with Chase Combining (HARQ-CC) aided Non-Orthogonal Multiple Access (NOMA) network. Specifically, an AoI minimization problem is formulated as a Markov Decision Process (MDP) problem. Then, to achieve deterministic, age-optimal, and intelligent power allocations and retransmission decisions, the Double-Dueling-Deep Q Network (DQN) is adopted. Furthermore, a more flexible retransmission scheme, referred to as Retransmit-At-Will scheme, is proposed to further facilitate the timeliness of the HARQ-aided NOMA network. Simulation results verify the superiority of the proposed intelligent scheme and demonstrate the threshold structure of the retransmission policy. Also, answers to whether user pairing is necessary are discussed by extensive simulation results.