Robotic grasping is a fundamental yet crucial component of robotic applications, as effective grasping often serves as the starting point for various tasks. With the rapid advancement of neural networks, data-driven approaches for robotic grasping have become mainstream. However, efficiently generating grasp datasets for training remains a bottleneck. This is compounded by the diverse structures of robotic hands, making the design of generalizable grasp generation methods even more complex. In this work, we propose a teleoperation-based framework to collect a small set of grasp pose demonstrations, which are augmented using FSG--a Fingertip-contact-aware Sampling-based Grasp generator. Based on the demonstrated grasp poses, we propose AutoWS, which automatically generates structured workspace clouds of robotic fingertips, embedding the hand structure information directly into the clouds to eliminate the need for inverse kinematics calculations. Experiments on grasping the YCB objects show that our method significantly outperforms existing approaches in both speed and valid pose generation rate. Our framework enables real-time grasp generation for hands with arbitrary structures and produces human-like grasps when combined with demonstrations, providing an efficient and robust data augmentation tool for data-driven grasp training.