Significance While adult brains are known to be functionally flexible, the emergence of a functionally flexible brain during early infancy is largely uncharted due the lack of approaches to assess neural flexibility in infants. Using recent advances of multilayer network approaches and a cohort of typically developing children who underwent longitudinal MRI during the first 2 y of life, we investigated the developmental characteristics of brain neural flexibility. The temporal and spatial emergence of a functionally flexible brain was revealed. Brain regions with high neural flexibility appear consistent with the core regions supporting cognitive flexibility processing in adults, whereas brain regions governing basic brain functions exhibit lower neural flexibility, demonstrating the emergence of functionally flexible brain during early infancy.