When a program is uninstalled, it often leaves remnants of itself behind in the Windows Registry. These aren't files exactly, but data entries that need to be cleared if the program is to be re-installed because otherwise the remnants can get in the way. A good way to do that is to use a third party Registry cleaner such as
Piriform's CCleaner (the free version is fine).
The above does assume Windows, of course. If you are working with the macOS version of Origin and the game, then things needs to be handled a bit differently.
If that's not it though, then you may need to seek further assistance on EA's Answers.HQ Origin board as this is really more of an Origin behavior issue than a game-related one.