Matching plays an important role in the logical allocation of resources across a wide range of industries. The benefits of matching have been increasingly recognized in manufacturing industries. In particular, capacity sharing has received much attention recently. In this paper, we consider the problem of dynamically matching demand-capacity types of manufacturing resources. We formulate the multi-period, many-to-many manufacturing resource-matching problem as a sequential decision process. The formulated manufacturing resource-matching problem involves large state and action spaces, and it is not practical to accurately model the joint distribution of various types of demands. To address the curse of dimensionality and the difficulty of explicitly modeling the transition dynamics, we use a model-free deep reinforcement learning approach to find optimal matching policies. Moreover, to tackle the issue of infeasible actions and slow convergence due to initial biased estimates caused by the maximum operator in Q-learning, we introduce two penalties to the traditional Q-learning algorithm: a domain knowledge-based penalty based on a prior policy and an infeasibility penalty that conforms to the demand-supply constraints. We establish theoretical results on the convergence of our domain knowledge-informed Q-learning providing performance guarantee for small-size problems. For large-size problems, we further inject our modified approach into the deep deterministic policy gradient (DDPG) algorithm, which we refer to as domain knowledge-informed DDPG (DKDDPG). In our computational study, including small- and large-scale experiments, DKDDPG consistently outperformed traditional DDPG and other RL algorithms, yielding higher rewards and demonstrating greater efficiency in time and episodes.