While foundation models have achieved remarkable results across a diversity of domains, they still rely on human-generated data, such as text, as a fundamental source of knowledge. However, this data is ultimately the product of human brains, the filtered projection of a deeper neural complexity. In this paper, we explore a new strategy for artificial intelligence: moving beyond surface-level statistical regularities by training foundation models directly on human brain data. We hypothesize that neuroimaging data could open a window into elements of human cognition that are not accessible through observable actions, and argue that this additional knowledge could be used, alongside classical training data, to overcome some of the current limitations of foundation models. While previous research has demonstrated the possibility to train classical machine learning or deep learning models on neural patterns, this path remains largely unexplored for high-level cognitive functions. Here, we classify the current limitations of foundation models, as well as the promising brain regions and cognitive processes that could be leveraged to address them, along four levels: perception, valuation, execution, and integration. Then, we propose two methods that could be implemented to prioritize the use of limited neuroimaging data for strategically chosen, high-value steps in foundation model training: reinforcement learning from human brain (RLHB) and chain of thought from human brain (CoTHB). We also discuss the potential implications for agents, artificial general intelligence, and artificial superintelligence, as well as the ethical, social, and technical challenges and opportunities. We argue that brain-trained foundation models could represent a realistic and effective middle ground between continuing to scale current architectures and exploring alternative, neuroscience-inspired solutions.