Reinforcement learning in partially observable environments is typically challenging, as it requires agents to learn an estimate of the underlying system state. These challenges are exacerbated in multi-agent settings, where agents learn simultaneously and influence the underlying state as well as each others' observations. We propose the use of learned beliefs on the underlying state of the system to overcome these challenges and enable reinforcement learning with fully decentralized training and execution. Our approach leverages state information to pre-train a probabilistic belief model in a self-supervised fashion. The resulting belief states, which capture both inferred state information as well as uncertainty over this information, are then used in a state-based reinforcement learning algorithm to create an end-to-end model for cooperative multi-agent reinforcement learning under partial observability. By separating the belief and reinforcement learning tasks, we are able to significantly simplify the policy and value function learning tasks and improve both the convergence speed and the final performance. We evaluate our proposed method on diverse partially observable multi-agent tasks designed to exhibit different variants of partial observability.