Transfer and adaptation to new unknown environmental dynamics is a key challenge for reinforcement learning (RL). An even greater challenge is performing near-optimally in a single attempt at test time, possibly without access to dense rewards, which is not addressed by current methods that require multiple experience rollouts for adaptation. To achieve single episode transfer in a family of environments with related dynamics, we propose a general algorithm that optimizes a probe and an inference model to rapidly estimate underlying latent variables of test dynamics, which are then immediately used as input to a universal control policy. This modular approach enables integration of state-of-the-art algorithms for variational inference or RL. Moreover, our approach does not require access to rewards at test time, allowing it to perform in settings where existing adaptive approaches cannot. In diverse experimental domains with a single episode test constraint, our method significantly outperforms existing adaptive approaches and shows favorable performance against baselines for robust transfer.