This article analyzes the Creches e Centros de Atendimento à Infância Caxiense (CCAIC) program, an intersectoral proposal for food and nutrition security, in the city of Duque de Caxias, Baixada Fluminense in the State of Rio de Janeiro, Brazil, which has children’s malnutrition or nutritional risk as an enrollment criterion. First, we present a historical outline of this public policy to combat malnutrition. Next, we bring some research findings from the diagnostic evaluation of the public education network. Finally, we analyze the possible effects of this policy in guaranteeing the right to access kindergarten and discuss possible demands for an intersectoral policy for the care of babies and children. We explore the dilemmas and tensions of this policy aiming to mitigate poverty, such as the production of a prejudiced look at babies, children, and their families; the multidimensionality of eating, extrapolating a physical perspective of nutrients in the food discussion; the crystallization of enrollment criteria, naturalizing the commitment of constitutional precepts and the principle of equality that guarantee Early Childhood Education for all children. Thus, this work sought to question how the CCAIC policy has understood the social demands of babies, children, and families and its effects on their lives.