The concept of neuromuscular activity recognition using instantaneous high-density surface electromyography (HD-sEMG) images opens up new avenues for the development of more fluid and natural muscle-computer interfaces. However, the existing approaches employed a very large deep convolutional neural network (ConvNet) architecture and complex training schemes for HD-sEMG image recognition, which requires the network architecture to be pre-trained on a very large-scale labeled training dataset, as a result, it makes computationally very expensive. To overcome this problem, we propose S-ConvNet and All-ConvNet models, a simple yet efficient framework for learning instantaneous HD-sEMG images from scratch for neuromuscular activity recognition. Without using any pre-trained models, our proposed S-ConvNet and All-ConvNet demonstrate very competitive recognition accuracy to the more complex state of the art for neuromuscular activity recognition based on instantaneous HD-sEMG images, while using a ~ 12 x smaller dataset and reducing learning parameters to a large extent. The experimental results proved that the S-ConvNet and All-ConvNet are highly effective for learning discriminative features for instantaneous HD-sEMG image recognition especially in the data and high-end resource constrained scenarios.