The COVID-19 pandemic significantly changed patterns of human interaction, including in the educational sector, which was forced to transform relationships among students, families, and the academic community. The present study sought to establish the interrelationships between performance on cognitive tests during the preschool stage and the perceptions of parents about remote education in school children during the pandemic. The study included 100 preschool children from socially vulnerable sectors who underwent remote and distance learning in 2020 and 2021. The reliability of the applied questionnaire was determined through a confirmatory factor analysis. A structural equation model was constructed to determine the perceptions of parents about remote education based on cognitive performance during the preschool stage. The model fit yielded favorable results for predictive variables (χ2 = 7.734, DF = 9 [p = 0.561], the comparative goodness-of-fit index [CFI] = 1.000, root mean square error of approximation [RMSEA] = 0.000, standardized mean square residual [SRMR] = 0.069), and executive function (χ2 = 3.711, DF = 5 [p > 0.592], CFI = 1.000, RMSEA = 0.000, SRMR = 0.039) as latent variables that affected parents’ perceptions. These results indicate that parents’ perceptions of remote education are mediated by predictive aspects of learning and executive function during the preschool stage.