This paper reports 2D and 3D direct numerical simulations of the Rayleigh-Bénard convection in a fluid layer, 3He, close to its gas-liquid critical point. The main quantity of interest is the time when the convective motion becomes appreciable after the heat current has been started. A space periodic, time-independent temperature perturbation is applied to the top plate aiming to represent the various sources of noise in the experiments. A single amplitude of this additional perturbation reproduces the noise level of the experiments for all the used combinations of the critical point proximity and of the heating power. Over four decades of the Rayleigh number, this simple operation removes the systematic discrepancy reported in an earlier paper and brings the simulations into good agreement with the measurements. Scaling of the exponential convection growth rate is presented and discussed.