Multi-fingered robotic hands could enable robots to perform sophisticated manipulation tasks. However, teaching a robot to grasp objects with an anthropomorphic hand is an arduous problem due to the high dimensionality of state and action spaces. Deep Reinforcement Learning (DRL) offers techniques to design control policies for this kind of problems without explicit environment or hand modeling. However, training these policies with state-of-the-art model-free algorithms is greatly challenging for multi-fingered hands. The main problem is that an efficient exploration of the environment is not possible for such high-dimensional problems, thus causing issues in the initial phases of policy optimization. One possibility to address this is to rely on off-line task demonstrations. However, oftentimes this is incredibly demanding in terms of time and computational resources. In this work, we overcome these requirements and propose the A Grasp Pose is All You Need (G-PAYN) method for the anthropomorphic hand of the iCub humanoid. We develop an approach to automatically collect task demonstrations to initialize the training of the policy. The proposed grasping pipeline starts from a grasp pose generated by an external algorithm, used to initiate the movement. Then a control policy (previously trained with the proposed G-PAYN) is used to reach and grab the object. We deployed the iCub into the MuJoCo simulator and use it to test our approach with objects from the YCB-Video dataset. The results show that G-PAYN outperforms current DRL techniques in the considered setting, in terms of success rate and execution time with respect to the baselines. The code to reproduce the experiments will be released upon acceptance.