The objective of the research is twofold. The study examines the role of public finance in promoting sustainable development in SSA. Secondly, the study investigates the optimal level of public finance beyond which public finance crowds out investment and hinders sustainable development in SSA. The study adopts a battery of econometric techniques such as the traditional ordinary least square (OLS) estimation technique, Driscoll-Kraay covariance matrix estimator, and the dynamic panel threshold model. The study found that an increase in public debts lead to a decline in sustainable development. In contrast, the results show that increase in spending on health and education, and tax can engender sustainable development in SSA. Further, we uncover the optimal levels of public spending on health and education, and public debts that engenders sustainable development in SSA. One main implication of the findings is that governments across SSA needs to reduce public debts levels and increase public spending on health and education to within the threshold levels established in this study to aid sustainable development in SSA.