This paper addresses the problem of synthesizing simulated humanoid climbing movements given the target holds, e.g., by the player of a climbing game. We contribute the first deep reinforcement learning solution that can handle interactive physically simulated humanoid climbing with more than one limb switching holds at the same time. A key component of our approach is Self-Supervised Episode State Initialization (SS- ESI), which ensures diverse exploration and speeds up learning, compared to a baseline approach where the climber is reset to an initial pose after failure. Our results also show that training with a multi-step action parameterization can produce both smoother movements and enable learning from slightly fewer explored actions at the cost of increased simulation time per action.