Interface resolving, multi-phase simulations with phase changes have been advancing to more and more complex problems supported by increases in computer power. These numerical investigations have allowed deeper insights into the conditions and important parameters controlling the surface heat flux as compared to previous techniques. While these numerical investigations directly predict important parameters such as bubble departure diameter and frequency that directly affect the average surface heat flux, cannot capture features which depend strongly on the surface morphology and cannot be resolved due to practical limitations of the differences in scale. A general approach to closure has been to choose an empirical approximation of the vapor bubble nucleation frequency for a given configuration and apply this constant value globally to all activated nucleation sites. Some have also varied the globally applied vapor bubble nucleation frequency as a parameter sensitivity and have demonstrated that the vapor bubble waiting period is an important parameter in determining the vapor bubble growth pattern. Therefore, a sub-grid nucleation model is needed to resolve the localized critical initiation of a vapor bubble from a given activated nucleation site (i.e., waiting time) and duration of vapor bubble growth to a resolved grid size (i.e., bubble growth) in the numerical simulation in order to resolve the impact of this key modeling uncertainty. In this work we report an efficient and numerically stable model that is generally applicable to vapor bubble dynamics at the unresolved length scales finer than the numerical grid used in interface resolving computational fluid dynamics simulations of nucleate pool boiling. It is based on a simplified energy and force balance on the extant vapor bubble retained in a micro-cavity. The inception of vapor bubble growth considers local thermodynamic effects and surface conditions and is formulated as a renewal time. Care has been taken to provide a numerically stable and computationally efficient closure. Detailed validation and application of the model in pool boiling applications will be provided in the full paper.