This study explored young children’s (2–8 years old) daily activities during the first lockdown with the outbreak of the COVID-19 pandemic (spring/2020, T1) and a year later (spring/2021, T2) from a cross-cultural perspective. It describes parent–child literacy and digital activities in Bulgaria, Israel, and Spain. Participating parents (747 in T1 and 432 in T2) answered online questionnaires about the frequency of parent–child literacy activities (alphabetic, book reading, and play) and digital activities (joint activities, selecting content, scaffolding) and the child’s screen time. The findings indicated moderate parent–child literacy and digital activities during the time points. A series of ANCOVAs revealed differences between time periods and cultures beyond the demographic measures (child’s age, parent’s education and age, and family size). During the first lockdown, parent–child joint digital activities and the child’s screen time were higher than a year later. A year later, parents were more involved in book reading, literacy play activities, and scaffolding their children’s use of digital devices. Interactions between the period and culture showed that Bulgarian and Spanish parents were more involved in their children’s literacy and digital activities than Israeli parents. Spanish children had more independent screen time than Bulgarian and Israeli children. Associations between literacy and digital activities implied a consistent parenting style across the activities.