@erinlive I somehow missed your reply earlier; sorry about that. When Origin keeps redownloading a game, the issue is usually Origin's cache, and occasionally an issue with the game files themselves. If you uninstalled Origin the normal way, try clearing its cache (again), then repairing or updating, or both, Sims 4 one more time.
If that doesn't help, please disable your antivirus, at least temporarily. It may be interfering with the game files—I've even seen Avast outright delete, or perhaps prevent from downloading, TS4_x64.exe, which of course would need to be present for the game to open at all.