Theory of Mind (ToM), the ability to attribute beliefs, intentions, or mental states to others, is a crucial feature of human social interaction. In complex environments, where the human sensory system reaches its limits, behaviour is strongly driven by our beliefs about the state of the world around us. Accessing others' mental states, e.g., beliefs and intentions, allows for more effective social interactions in natural contexts. Yet, these variables are not directly observable, making understanding ToM a challenging quest of interest for different fields, including psychology, machine learning and robotics. In this paper, we contribute to this topic by showing a developmental synergy between learning to predict low-level mental states (e.g., intentions, goals) and attributing high-level ones (i.e., beliefs). Specifically, we assume that learning beliefs attribution can occur by observing one's own decision processes involving beliefs, e.g., in a partially observable environment. Using a simple feed-forward deep learning model, we show that, when learning to predict others' intentions and actions, more accurate predictions can be acquired earlier if beliefs attribution is learnt simultaneously. Furthermore, we show that the learning performance improves even when observed actors have a different embodiment than the observer and the gain is higher when observing beliefs-driven chunks of behaviour. We propose that our computational approach can inform the understanding of human social cognitive development and be relevant for the design of future adaptive social robots able to autonomously understand, assist, and learn from human interaction partners in novel natural environments and tasks.