When you download an offline map using the OfflineMapTask, Runtime will create a folder at the location you specify when you create the new GenerateOfflineMapJob, and will download and write a number of resources into that folder. As you noticed, there is a .mmap file, but you should consider the folder to be a black box.
To re-use the already downloaded offline map, as @JoeHershman shows below, you create a new MobileMapPackage with the same folder you specified when you downloaded the offline map. Then get the first map from it. See this documentation for more info.
Note, you do not need to explicitly load the map or its operational layers unless you plan on reading their metadata before they are displayed in a map view.