Cross-subject motor imagery (CS-MI) classification in brain-computer interfaces (BCIs) is a challenging task due to the significant variability in Electroencephalography (EEG) patterns across different individuals. This variability often results in lower classification accuracy compared to subject-specific models, presenting a major barrier to developing calibration-free BCIs suitable for real-world applications. In this paper, we introduce a novel approach that significantly enhances cross-subject MI classification performance through optimized preprocessing and deep learning techniques. Our approach involves direct classification of Short-Time Fourier Transform (STFT)-transformed EEG data, optimized STFT parameters, and a balanced batching strategy during training of a Convolutional Neural Network (CNN). This approach is uniquely validated across four different datasets, including three widely-used benchmark datasets leading to substantial improvements in cross-subject classification, achieving 67.60% on the BCI Competition IV Dataset 1 (IV-1), 65.96% on Dataset 2A (IV-2A), and 80.22% on Dataset 2B (IV-2B), outperforming state-of-the-art techniques. Additionally, we systematically investigate the classification performance using MI windows ranging from the full 4-second window to 1-second windows. These results establish a new benchmark for generalizable, calibration-free MI classification in addition to contributing a robust open-access dataset to advance research in this domain.