Many climate processes are characterized using large systems of nonlinear differential equations; this, along with the immense amount of data required to parameterize complex interactions, means that Earth-System Model (ESM) simulations may take weeks to run on large clusters. Uncertainty quantification may require thousands of runs, making ESM simulations impractical for preliminary assessment. Alternatives may include simplifying the processes in the model, but recent efforts have focused on using machine learning to complement these models or even act as full surrogates. \textit{We leverage machine learning, specifically fully-connected neural networks (FCNNs) and graph convolutional neural networks (GCNNs), to enable rapid simulation and uncertainty quantification in order to inform more extensive ESM simulations.} Our surrogate simulated 80 years in approximately 310 seconds on a single A100 GPU, compared to weeks for the ESM model while having mean temperature errors below and maximum errors below .