The study examines students' skills at kindergarten entry and gains in skills across the kindergarten through first-grade period (pre-COVID-19) for predicting literacy, language, math, inhibitory control, and social-adjustment outcomes in the spring of fourth grade, after schools reopened. In a large US school district, longitudinal data were collected on students (N = 785) who were linguistically diverse (85% home language other than English) and from families with low-income backgrounds. Adjusting for covariates, students' achievement and executive function skills at entry to kindergarten and gains in these skills across K-1 predicted their proficiency in reading, math, and language in fourth grade. Executive function skills at kindergarten entry and across K-1 predicted inhibitory control in fourth grade, and kindergarten-entry social adjustment predicted school engagement and connectedness to teachers in fourth grade. Early skills or gains were not differentially predictive of fourth-grade outcomes for English-language learners versus English speakers.