Aim: The aim of this study was to identify the factors influencing preschool children’s daily smartphone and tablet use and to evaluate the relative importance of these factors using machine learning models. Furthermore, the findings were discussed within the framework of Bandura’s Social Learning Theory to examine the parental and environmental influences shaping children’s screen time. Methods: This study was conducted in a district of Central Anatolia, Turkey, with data collected from the parents of children aged 4–6 years (N = 266). The data included children’s daily screen time, purposes of device use, and parental digital habits. Analyses were performed using logistic regression, support vector machines, artificial neural networks, and XGBoost algorithms. Model performance was compared in terms of accuracy, F1 score, sensitivity, specificity, and area under the ROC curve values. Feature importance was also examined. Results: The child’s purpose of device use was found to be the strongest predictor of screen time. In particular, using devices for educational content and turning to devices when bored were the most prominent determinants. Parents’ daily screen use exceeding 3 hours and frequent social media use also significantly increased children’s screen time. Parental guidance behaviors (e.g., coviewing content and setting limits) showed significant effects, whereas demographic factors contributed to a lesser extent. Conclusion: The study demonstrates that children’s screen time is shaped not only by demographic characteristics but also by usage purposes and parental digital habits. It is recommended that parents act as role models, provide guidance in content selection, and enforce restrictions during critical periods.