When porous media saturated with initially stagnant cold water around the density maximum temperature are cooled from above, convection may be induced in an unstable lower layer. In this study, the onset of buoyancy-driven convection during time-dependent cooling is investigated using the propagation theory, which transforms disturbance equations similarly, and also considering the density inversion effect. The critical Darcy-Rayleigh number Ra-D,Ra-c is found as a function of the dimensionless density maximum temperature theta(max). For Ra-D > Ra-D,Ra-c the dimensionless critical time tau(c) to mark the onset of instability is presented as a function of Ra-D and theta(max). These critical conditions are compared with previous theoretical results.