During the ignition of a swirled single-injector combustor, two phases have been identified experimentally. In the first, the flame penetrates the injection unit, while in the second the flame lifts off after a substantial delay before stabilizing at a distance from the injector. This transient phenomenon is investigated using Large Eddy Simulations based on an Euler-Lagrange description of the liquid spray, an energy deposition model to mimic ignition and the thickened flame combustion model. It is shown that the initial penetration of the flame in the injector unit is linked with the positive pressure excursion induced by the rapid volumetric expansion of burnt gases. This sudden expansion is itself due to the fast increase in heat release rate that occurs during the initiation of the process. The corresponding positive and negative pressure disturbances induce a rapid reduction of the mass flow rate through the injector, followed by an acceleration of the flow and a return to the nominal value. It is also shown that the flame root disappears after another delay, which results in the flame edge lifting and stabilization at a distance from the injector exhaust corresponding to steady operation of the device. The relatively long delay time before this lift-off takes place is found to correspond to the residence time of the cooled burnt gases in the vicinity of the chamber walls, which are ultimately entrained by the internal recirculation zone and quench the lower flame foot.