Coalescence is a complex phenomenon leading to the merging of deformable particles of fluid. The complexity stems largely from the simultaneous occurrence of phenomena of a different nature (hydrodynamic, electrostatic, physicochemical) acting at different scales. The stochastic effects controlling the formation of the liquid bridge between two droplets of the same liquid, immersed in another nonmiscible liquid, are studied through a series of molecular dynamics simulations. The case of heptane droplets in water, relevant to solvent extraction, a key process of the circular economy, is considered. From this series of simulations, we have confirmed that the probability function of coalescence of two identical droplets in contact follows a Poisson distribution. We moreover propose a criterion for the initiation of coalescence based on nucleation theory. A complete description of the stochastic initiation of coalescence is hence provided, opening many perspectives for the simulation of coalescence in continuous approaches used in fluid mechanics and chemical engineering. The methodology can be generalized to droplets of different size and composition, immersed in gas, or to bubbles, i.e., to other physical problems whose kinetics is influenced by the molecular scale.