We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number R a^ s. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness δ* at the onset of convection. We show that the dimensionless boundary layer thickness δ= δ*/d scales as R a s− p, where R a s= R a^ s δ is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p= 0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.