Experiments have shown that an overcritical density plasma is typically identified in some specific regions in conventional microwave (MW) discharges. The present work theoretically investigates this problem in a new and thorough way. By solving the wave equation, we treat the dynamic behaviour of the MW fields propagating through a gas slab. In this case, the gas is ionized and the density of the produced plasma grows consequently with time. Generalizing the results to a semi-infinite space case, we obtain the wave reflection index of the produced plasma. Comparison with the steady state case shows that the derived unsteady reflection index approaches its steady state value only at a very slow growth of the plasma density. This difference with the steady state values also leads to the deflection of the cut-off frequency from its usual value. At the critical plasma density, ncr, the reflection index of the unsteady produced plasma is estimated to be much less than unity, which results in much more penetration of the wave and also ionization of the gas. We show that the density of the overcritical plasma, produced in this way, may reach approximately 15ncr.