X-ray absorption spectroscopy (XAS) is a powerful characterization technique for probing the local chemical environment of absorbing atoms. However, analyzing XAS data presents with significant challenges, often requiring extensive, computationally intensive simulations, as well as significant domain expertise. These limitations hinder the development of fast, robust XAS analysis pipelines that are essential in high-throughput studies and for autonomous experimentation. We address these challenges with a suite of transfer learning approaches for XAS prediction, each uniquely contributing to improved accuracy and efficiency, as demonstrated on K-edge spectra database covering eight 3d transition metals (Ti-Cu). Our framework is built upon three distinct strategies. First, we use M3GNet to derive latent representations of the local chemical environment of absorption sites as input for XAS prediction, achieving up to order-of-magnitude improvements over conventional featurization techniques. Second, we employ a hierarchical transfer learning strategy, training a universal multi-task model across elements before fine-tuning for element-specific predictions. This cascaded approach after element-wise fine-turning yields models that outperform element-specific models by up to 31\%. Third, we implement cross-fidelity transfer learning, adapting a universal model to predict spectra generated by simulation of a different fidelity with a much higher computational cost. This approach improves prediction accuracy by up to 24\% over models trained on the target fidelity alone. Our approach is extendable to XAS prediction for a broader range of elements and offers a generalizable transfer learning framework to enhance other deep-learning models in materials science.