When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number Oh, the dynamics of the bridge differs a lot. For Oh ≈ 1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge centre. The expansion is thus caused by the capillary pressure that drives the fluid towards the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of non-dispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result of the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow-rate that enters the bridge and thus determines its radial expansion.