Hypoxic-Ischemic Encephalopathy (HIE) affects 1 to 5 out of every 1,000 newborns, with 30% to 50% of cases resulting in adverse neurocognitive outcomes. However, these outcomes can only be reliably assessed as early as age 2. Therefore, early and accurate prediction of HIE-related neurocognitive outcomes using deep learning models is critical for improving clinical decision-making, guiding treatment decisions and assessing novel therapies. However, a major challenge in developing deep learning models for this purpose is the scarcity of large, annotated HIE datasets. We have assembled the first and largest public dataset, however it contains only 156 cases with 2-year neurocognitive outcome labels. In contrast, we have collected 8,859 normal brain black Magnetic Resonance Imagings (MRIs) with 0-97 years of age that are available for brain age estimation using deep learning models. In this paper, we introduce AGE2HIE to transfer knowledge learned by deep learning models from healthy controls brain MRIs to a diseased cohort, from structural to diffusion MRIs, from regression of continuous age estimation to prediction of the binary neurocognitive outcomes, and from lifespan age (0-97 years) to infant (0-2 weeks). Compared to training from scratch, transfer learning from brain age estimation significantly improves not only the prediction accuracy (3% or 2% improvement in same or multi-site), but also the model generalization across different sites (5% improvement in cross-site validation).