Hyperspectral image (HSI) classification typically involves large-scale data and computationally intensive training, which limits the practical deployment of deep learning models in real-world remote sensing tasks. This study introduces SpectralTrain, a universal, architecture-agnostic training framework that enhances learning efficiency by integrating curriculum learning (CL) with principal component analysis (PCA)-based spectral downsampling. By gradually introducing spectral complexity while preserving essential information, SpectralTrain enables efficient learning of spectral -- spatial patterns at significantly reduced computational costs. The framework is independent of specific architectures, optimizers, or loss functions and is compatible with both classical and state-of-the-art (SOTA) models. Extensive experiments on three benchmark datasets -- Indian Pines, Salinas-A, and the newly introduced CloudPatch-7 -- demonstrate strong generalization across spatial scales, spectral characteristics, and application domains. The results indicate consistent reductions in training time by 2-7x speedups with small-to-moderate accuracy deltas depending on backbone. Its application to cloud classification further reveals potential in climate-related remote sensing, emphasizing training strategy optimization as an effective complement to architectural design in HSI models. Code is available at https://github.com/mh-zhou/SpectralTrain.