There is another post but that has a lot of trial & error steps to slog through. I’m not a user of the Media feature but I’ll try to boil it down until a more Media experienced user comes online. (Tonite, you’re the beneficiary of a bit of insomnia.)
(Fortunately, you’ve done the hard part to explain, putting/downloading the files into a folder and setting the Media base path.)
You can use the Media Verify tool (this is a free add-on) to find the images in the new base path location.
This tool will scour the subdirectories of the basepaths too. So the collection hierarchy of folders doesn’t have to be ‘flattened’.