The Faraday instability arising in distinct miscible fluid layers, when the parametric forcing is parallel to the gravity vector, is analysed. A time-dependent density gradient is established from the moment the fluid layers are placed in contact with one another. The operating parameters in a miscible Faraday system are the frequency of parametric forcing and the wait time between the initial contact of fluids and the commencement of oscillations. Using a linearized theory that invokes a quasi-steady approximation, the vibrational threshold required for the onset of Faraday instability is evaluated for these parameters and several observations are made. First, the criticality is observed to occur at a sub-harmonic frequency. Second, the large magnitude of the concentration gradient at early wait times is found to make the thin layers highly unstable. Third, the stability increases with forcing frequency, owing to the increased dissipation of the resulting choppy waves. All these observations qualitatively agree with experiments. Finally, a calculation reveals that an increase in gravity increases the critical wavelength of flow onset and results in the reduction of critical input acceleration. (C) 2015 AIP Publishing LLC.