A conventional brain-computer interface (BCI) requires a complete data gathering, training, and calibration phase for each user before it can be used. This preliminary phase is time-consuming and should be done under the supervision of technical experts commonly in laboratories for the BCI to function properly. In recent years, a number of subject-independent (SI) BCIs have been developed. However, there are many problems preventing them from being used in real-world BCI applications. A lower accuracy than the subject-dependent (SD) approach and a relatively high run-time of models with a large number of model parameters are the most important ones. Therefore, a real-world BCI application would greatly benefit from a compact subject-independent BCI framework, ready to use immediately after the user puts it on, and suitable for low-power edge-computing and applications in the emerging area of internet of things (IoT). We propose a novel subject-independent BCI framework named CCSPNet (Convolutional Common Spatial Pattern Network) that is trained on the motor imagery (MI) paradigm of a large-scale EEG signals database consisting of 400 trials for every 54 subjects performing two-class hand-movement MI tasks. The proposed framework applies a wavelet kernel convolutional neural network (WKCNN) and a temporal convolutional neural network (TCNN) in order to represent and extract the diverse frequency behavior and spectral patterns of EEG signals. The convolutional layers outputs go through a CSP algorithm for class discrimination and spatial feature extraction. The number of CSP features is reduced by a dense neural network, and the final class label is determined by an LDA. The final SD and SI classification accuracies of the proposed framework match the best results obtained on the largest motor-imagery dataset present in the BCI literature, with 99.993 percent fewer model parameters.