The identification of threshold in nanolasers still poses not entirely met challenges. Dynamical techniques offer interesting methods to determine the achievement of coherent emission. A recent experimental proposal rests on the dynamical shift of a bifurcation in the presence of a modulated pump indirectly observed through the study of the behaviour of the zero–delay second–order autocorrelation function of the detected photon number. This paper investigates the potential for directly observing the dynamical hysteresis which accompanies the sweep across threshold in a large β nanolaser. We conclude that the observation is possible in principle, but that the experiment has to be carefully designed to achieve this goal.