Intention recognition has traditionally focused on individual intentions, overlooking the complexities of collective intentions in group settings. To address this limitation, we introduce the concept of group intention, which represents shared goals emerging through the actions of multiple individuals, and Group Intention Forecasting (GIF), a novel task that forecasts when group intentions will occur by analyzing individual actions and interactions before the collective goal becomes apparent. To investigate GIF in a specific scenario, we propose SHOT, the first large-scale dataset for GIF, consisting of 1,979 basketball video clips captured from 5 camera views and annotated with 6 types of individual attributes. SHOT is designed with 3 key characteristics: multi-individual information, multi-view adaptability, and multi-level intention, making it well-suited for studying emerging group intentions. Furthermore, we introduce GIFT (Group Intention ForecasTer), a framework that extracts fine-grained individual features and models evolving group dynamics to forecast intention emergence. Experimental results confirm the effectiveness of SHOT and GIFT, establishing a strong foundation for future research in group intention forecasting. The dataset is available at https://xinyi-hu.github.io/SHOT_DATASET.