You can set Firefox browser's preference to save a file automatically, and not let the download window popup. Then you will be able to just grab the file, and it'll start getting downloaded.
So, something like this:
FirefoxProfile fxProfile = new FirefoxProfile();
WebDriver driver = new FirefoxDriver(fxProfile);
and given that you now have the download directory, it will not ask you to save the file, and no download manager would appear, as automation from this point would be straightforward.
I hope this helps!