This study investigated the impact of storage conditions of the ingredients for yogurt production on the rheological and physicochemical characteristics of the final fermented product. The novelty is the application of a special mix of milk protein concentrate and sodium caseinate for yogurt production. Separately exposing the protein mix powder and bacteria culture to 20 °C caused considerable changes in the obtained yogurt stiffness and the incubation times required to produce the gel due to a decrease in bacterial count. Minimal changes in bacteria viability were observed after storage at 5 °C. Lower temperature and shorter storage times increased yogurt firmness, viscosity, and storage modulus, resulting in a smoother and more viscous product. A linear correlation was found between yogurt firmness and water activity. Powders stored at lower temperatures and for shorter times produced yogurt with stronger texture and better water binding. Additionally, yogurt obtained from dry ingredients stored under these conditions required shorter incubation times. Storing the starter culture at 5 °C for at least 8 weeks had no significant effects on the physicochemical properties or incubation time requited to produce the final yogurt. This work highlights the importance of storage conditions of yogurt dry ingredients in maintaining the quality of the final product.