No, you do not have to refrigerate your sourdough starter if it's not activated yet. In fact, it's best to keep the starter at room temperature until it becomes active and established.
During the initial stages of creating a sourdough starter, you'll be combining flour and water to create an environment where wild yeast and bacteria can start to grow and ferment. These microorganisms are present in the flour and the surrounding environment. Keeping the starter at room temperature (around 70-75°F or 21-24°C) helps promote the growth of these beneficial microorganisms, allowing the starter to become active.
Once your starter is active and showing signs of fermentation (bubbles forming, increasing in volume), you can begin feeding it regularly to maintain its strength. At this point, if you don't plan to use the starter every day, you can transition to refrigerating it. Refrigeration significantly slows down the fermentation process, allowing you to feed the starter less frequently. When refrigerated, it's generally recommended to feed the starter at least once a week.
Remember, if you don't plan to bake with your starter for an extended period, you can refresh it, then refrigerate it for longer storage. When you want to bake, you'll need to take it out of the fridge, let it come to room temperature, and then feed it to activate and refresh it before using it in your sourdough recipe.