We report a time-resolved approach to probe the mechanical properties of thin films during drying and solidification based on surface wrinkling. The approach is demonstrated by measuring the modulus of a ternary system comprising an inorganic salt (aluminum chlorohydrate), a humectant (glycerol), and water across the glassy film formation pathway. The topography of mechanically induced wrinkling of supported films on polydimethylsiloxane (PDMS) is experimentally monitored during mechanical extension and relaxation cycles. Nontrivial aspects of our method include the need to oxidize the (hydrophobic) PDMS surface prior to solution deposition to enable surface wetting, which simultaneously creates a glassy-layer skin, whose wrinkling can contribute to the overall topography. Film drying is studied as a function of solution concentration and time, and a range of pattern morphologies are found: sinusoidal wrinkling, transient double-wavelength wrinkling accompanying film "crust" formation, ridging associated with stress localization, and cracking. We quantify the evolution of the elastic modulus during the sinusoidal wrinkling stage, employing bi- and trilayer models, which are independently confirmed by nanoindentation. The method provides thus a simple and robust approach for the mechanical characterization of out-of-equilibrium thin films.