High cavitating or supercavitating flows in fuel injector systems are crucial since they improve the mixing and the fuel atomization into combustion chambers, decreasing both fuel consumption and pollutant emissions. However, there is a lack of information regarding the required time to obtain high cavitating flows at the nozzle outlet, from the start of the injection pulse. In this work, a new method to quantify the time to get supercavitating flows at the nozzle outlet is developed. In particular, the delay in the inception of a supercavitating flow through a micronozzle is numerically analyzed for different pressure drops in a well-studied benchmark for fuel injectors. The three-dimensional simulations show that a delay higher than 100 μ s is necessary for moderate pressure drops. Nevertheless, the delay tends to decay by rising amplitudes of the pressure pulse, reaching a saturation value of around 65 μ s.