The study examines students' skills at kindergarten entry and gains in skills across kindergarten through first grade (pre-COVID) predicting literacy, language, math, inhibitory control, and social adjustment in the spring of 4th grade, after schools re-opened. 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 proficiency in reading, math, and language in 4th grade. Executive function skills at kindergarten entry and across k-1 predicted inhibitory control in 4th grade; social adjustment predicted school engagement and connectedness to teachers. Early skills or gains were not differentially predictive of 4th grade outcomes for English Language Learners. These findings reinforce the importance of experiences in the early school years that foster academic, executive function, and social skills. [This paper will be published in "Elementary School Journal."]