There is consensus about the positive effects of high quality Early Childhood Education and Care (ECEC) on children’s development, particularly for children from lower socioeconomic backgrounds. However, limited knowledge exists on the access to quality in ECEC in a universal context. This study investigates potential socioeconomic selection into ECEC of higher structural quality in the context of a universal, heavily subsidized, and regulated system in Norway, intended to provide equal access to high quality ECEC. Furthermore, we explore the impact of SES and structural quality in ECEC on student-teacher relationship quality. Our conceptual model takes into account how readily accessible information on different quality aspects is for parents. We use data from the Norwegian Mother, Father and Child Cohort Study linked with teacher-reported ECEC quality for children born in 2006–2009 (N 7,226), supplemented by registry data at ECEC and municipality level. We find that higher parental education, and to a lesser degree income, predict child attendance of ECEC with higher structural quality as rated by ECEC teachers. Further, higher parental SES and structural quality (i.e., developmental material, staff competence and stability) predict better student-teacher relationship quality in terms of higher level of closeness and less conflict. These findings suggest that ambitions of universal equal access to high quality ECEC are not entirely realized and more efforts are needed to ensure higher structural quality in ECEC and enhance relationship quality for children from less advantageous socioeconomic backgrounds.