Literacy acquisition is a complex process with genetic and environmental factors influencing cognitive and neural processes associated with reading. Previous research identified factors that predict word reading fluency (WRF), including phonological awareness (PA), rapid automatized naming (RAN), and speech‐in‐noise perception (SPIN). Recent theoretical accounts suggest dynamic interactions between these factors and reading, but direct investigations of such dynamics are lacking. Here, we investigated the dynamic effect of phonological processing and speech perception on WRF. More specifically, we evaluated the dynamic influence of PA, RAN, and SPIN measured in kindergarten (the year prior to formal reading instruction), first grade (the first year of formal reading instruction) and second grade on WRF in second and third grade. We also assessed the effect of an indirect proxy of family risk for reading difficulties using a parental questionnaire (Adult Reading History Questionnaire, ARHQ). We applied path modeling in a longitudinal sample of 162 Dutch‐speaking children of whom the majority was selected to have an increased family and/or cognitive risk for dyslexia. We showed that parental ARHQ had a significant effect on WRF, RAN and SPIN, but unexpectedly not on PA. We also found effects of RAN and PA directly on WRF that were limited to first and second grade respectively, in contrast to previous research reporting pre‐reading PA effects and prolonged RAN effects throughout reading acquisition. Our study provides important new insights into early prediction of later word reading abilities and into the optimal time window to target a specific reading‐related subskill during intervention.