In English we use the verb to discover to talk about information and things that are completely new. One can also use discover if you one is the first person to learn some new information. In the case of the mouse and cheese, the mouse would "find" the cheese.
I'd say that for mouse and cheese, מוצא is more natural, but מגלה can pass. I suspect the two verbs are just as close in English as they are in Hebrew, maybe just a slight different of habit between the two languages.