As one of the fast evolution of remote sensing and spectral imagery techniques, hyperspectral image (HSI) classification has attracted considerable attention in various fields, including land survey, resource monitoring, and among others. Nonetheless, due to a lack of distinctiveness in the hyperspectral pixels of separate classes, there is a recurrent inseparability obstacle in the primary space. Additionally, an open challenge stems from examining efficient techniques that can speedily classify and interpret the spectral-spatial data bands within a more precise computational time. Hence, in this work, we propose a 3D-2D convolutional neural network and transfer learning model where the early layers of the model exploit 3D convolutions to modeling spectral-spatial information. On top of it are 2D convolutional layers to handle semantic abstraction mainly. Toward simplicity and a highly modularized network for image classification, we leverage the ResNeXt-50 block for our model. Furthermore, improving the separability among classes and balance of the interclass and intraclass criteria, we engaged principal component analysis (PCA) for the best orthogonal vectors for representing information from HSIs before feeding to the network. The experimental result shows that our model can efficiently improve the hyperspectral imagery classification, including an instantaneous representation of the spectral-spatial information. Our model evaluation on five publicly available hyperspectral datasets, Indian Pines (IP), Pavia University Scene (PU), Salinas Scene (SA), Botswana (BS), and Kennedy Space Center (KSC), was performed with a high classification accuracy of 99.85%, 99.98%, 100%, 99.82%, and 99.71%, respectively. Quantitative results demonstrated that it outperformed several state-of-the-arts (SOTA), deep neural network-based approaches, and standard classifiers. Thus, it has provided more insight into hyperspectral image classification.