Gesture recognition using low-resolution instantaneous HD-sEMG images opens up new avenues for the development of more fluid and natural muscle-computer interfaces. However, the data variability between inter-session and inter-subject scenarios presents a great challenge. The existing approaches employed very large and complex deep ConvNet or 2SRNN-based domain adaptation methods to approximate the distribution shift caused by these inter-session and inter-subject data variability. Hence, these methods also require learning over millions of training parameters and a large pre-trained and target domain dataset in both the pre-training and adaptation stages. As a result, it makes high-end resource-bounded and computationally very expensive for deployment in real-time applications. To overcome this problem, we propose a lightweight All-ConvNet+TL model that leverages lightweight All-ConvNet and transfer learning (TL) for the enhancement of inter-session and inter-subject gesture recognition performance. The All-ConvNet+TL model consists solely of convolutional layers, a simple yet efficient framework for learning invariant and discriminative representations to address the distribution shifts caused by inter-session and inter-subject data variability. Experiments on four datasets demonstrate that our proposed methods outperform the most complex existing approaches by a large margin and achieve state-of-the-art results on inter-session and inter-subject scenarios and perform on par or competitively on intra-session gesture recognition. These performance gaps increase even more when a tiny amount (e.g., a single trial) of data is available on the target domain for adaptation. These outstanding experimental results provide evidence that the current state-of-the-art models may be overparameterized for sEMG-based inter-session and inter-subject gesture recognition tasks.