This study examines regional disparities and convergence dynamics in paediatric healthcare accessibility across Poland’s 16 provinces between 2010 and 2023. A synthetic Paediatric Service Accessibility Index (PSA Index), constructed with Hellwig’s method, is combined with socio-economic indicators such as employment, urbanisation, and disposable income to evaluate the alignment between healthcare provision and regional development. The analysis employs non-parametric regional tests (Spearman’s rank correlation, Wilcoxon signed-rank test) and national panel regression models (Fixed and Random Effects). Results demonstrate significant spatial heterogeneity: economically advanced regions, including Mazowieckie and Małopolskie, show moderate to strong convergence between socio-economic progress and healthcare access, whereas structurally weaker regions such as Lubuskie and Podkarpackie reveal persistent divergence. Disposable income and urbanisation emerge as significant predictors of healthcare availability (p < 0.01), while employment is not statistically significant. The findings highlight enduring inequalities that are relevant in the context of the European Union’s (EU) cohesion policy and indicate that economic growth alone is insufficient to ensure equitable access to paediatric care. Comparative evidence from Romania, Bulgaria, and Spain points to similar patterns and emphasises the importance of EU Structural and Investment Funds in promoting healthcare equity. The study concludes that territorially sensitive, multidimensional interventions are necessary to advance social sustainability and to align healthcare infrastructure with the Sustainable Development Goals, particularly SDG 3 (Good Health and Well-Being) and SDG 10 (Reduced Inequalities).