The Global Change Analysis Model (GCAM) simulates complex interactions between the coupled Earth and human systems, providing valuable insights into the co-evolution of land, water, and energy sectors under different future scenarios. Understanding the sensitivities and drivers of this multisectoral system can lead to more robust understanding of the different pathways to particular outcomes. The interactions and complexity of the coupled human-Earth systems make GCAM simulations costly to run at scale - a requirement for large ensemble experiments which explore uncertainty in model parameters and outputs. A differentiable emulator with similar predictive power, but greater efficiency, could provide novel scenario discovery and analysis of GCAM and its outputs, requiring fewer runs of GCAM. As a first use case, we train a deep learning model on an existing large ensemble that explores a range of GCAM inputs related to different relative contributions of energy production sources, with a focus on wind and solar. We complement this existing ensemble with interpolated input values and a wider selection of outputs, predicting 22,528 GCAM outputs across time, sectors, and regions. We report a median R^2 score of 0.998 for the emulator's predictions and an R^2 score of 0.812 for its input-output sensitivity.