Research on the longitudinal courses of child social–emotional symptoms and sleep during the COVID-19 pandemic within societies would be of key value for promoting child well-being in global crises. We characterized the course of children’s social–emotional and sleep symptoms before and throughout the pandemic in a Finnish longitudinal cohort of 1825 5- to 9-year-old children (46% girls) with four follow-up points during the pandemic from up to 695 participants (spring 2020–summer 2021). Second, we examined the role of parental distress and COVID-related stressful events in child symptoms. Child total and behavioral symptoms increased in spring 2020 but decreased thereafter and remained stable throughout the rest of the follow-up. Sleep symptoms decreased in spring 2020 and remained stable thereafter. Parental distress was linked with higher child social–emotional and sleep symptoms. The cross-sectional associations between COVID-related stressors and child symptoms were partially mediated by parental distress. The findings propose that children can be protected from the long-term adverse influences of the pandemic, and parental well-being likely plays a mediating role between pandemic-related stressors and child well-being. Further research focusing on the societal and resilience factors underlying family and child responses to the pandemic is warranted.