Objective: Electromyogram (EMG)-informed neuromusculoskeletal (NMS) models can predict physiologically plausible muscle forces and joint moments. However, calibrating model parameters (e.g., optimal fiber length, tendon slack length) to the individual is time-consuming, with the optimization often requiring hours to converge and typically not accounting for unrecorded muscle excitations. This study addresses these limitations by incorporating differentiable physics and muscle synergies into the calibration of NMS models. Methods: We implemented an NMS model with auto-differentiable Hill-type muscles, enabling the use of adaptive gradient descent optimizers. Two types of calibration were evaluated: a standard EMG-driven approach and a synergy-hybrid approach that also synthesized unrecorded excitations. These methods were evaluated using upper and lower limb data, each from a single participant. Results: The calibration time was reduced by up to 26 times while maintaining comparable accuracy in moment predictions. Compared to the EMG-driven calibration, the synergy-hybrid calibration improved the estimates of model parameters for reduced number of EMG channels. Conclusion: Autodifferentiable Hill-type muscle models greatly reduce NMS model calibration time and enables the synthesis of unrecorded muscle excitations through muscle synergies, facilitating the calibration of all muscle parameters. Significance: This new rapid calibration could support deployment of NMS models in time-sensitive applications, including real-time biomechanical analyses and personalized neurorehabilitation.