The onset of buoyancy-driven convection in an initially quiescent, horizontal silica nanoparticle suspension layer heated from above is analyzed theoretically. In this thermally-stably stratified fluid layer the Soret diffusion can induce buoyancy-driven motion for the case of the negative separation ratio. For the high Rayleigh number the convective motion sets in during the transient diffusion stage and the onset time of this motion is analyzed by employing the nonlinear numerical simulation. It is interesting that the convective motion is very weak and the diffusional process is dominant even after the onset time of convection, τc, and the nonlinear effects are manifested from the time τm(>τc). The present τm explains the existing experimental results quite well.