Background: The purpose of this study is to identify the factors that influence the parental role satisfaction of Korea fathers with young children (ages 1–3) in the COVID-19 endemic period. Methods: Data were collected from 172 Korea fathers of young children from March to May 2024, self-reported questionnaire using convenience sampling. Descriptive statistics, t-test, ANOVA (Analysis of Variance), correlation analysis and multiple regression were used to analyze the collected data. The Durbin-Watson value was 2.23, which is close to the ideal value of 2, indicating no significant autocorrelation in the error terms. Residual analysis also confirmed that the model met the assumptions of linearity, normality of error terms and homoscedasticity. Results: The regression model was found to be significant (F = 22.18, p = 0.004), with an explanatory power of 61.2%. The factors that most significantly influenced the parental role satisfaction of fathers with young children were found to be parenting behavior (β = 0.36, p = 0.009) and parenting stress (β = −0.22, p = 0.003). Conclusions: Parenting behaviors were positively related to paternal role satisfaction, while greater parenting stress was associated with lower paternal role satisfaction. To improve the parental role satisfaction of fathers with young children, it is important to encourage positive parenting behaviors and create support systems and programs to reduce parenting stress. Further research should focus on the impact of paternal involvement in the Korean context to build a comprehensive understanding of how fathers can receive support in their roles. By addressing these areas, policymakers and community programs can better support fathers, ultimately benefiting families and children in Korea.