The time of the onset of double-diffusive convection in time-dependent, nonlinear temperature fields is investigated theoretically. The initially quiescent horizontal fluid layer with a uniform solute gradient experiences ramp heating from below, but its stable solute concentration is to reduce thermal effects which invoke convective motion. The related stability analysis is conducted on the basis of the propagation theory. Under the linear stability theory the thermal penetration depth is used as a length scaling factor and the linearized perturbation equations of similarity transform are solved numerically. The resulting correlations of the critical time to mark the onset of regular cells are derived as a function of the thermal Rayleigh and the solute Rayleigh numbers. The predicted stability criteria are apparently consistent with existing experimental results for aqueous solution of sodium chloride.