@Izziekr I'm not sure whether you've ever installed TS3 on this computer, or any related files, but please check to make sure you don't have any hidden library files from the game. Here's how to find them:
https://bluebellflora.com/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
Once you've deleted everything TS3-related, please run the Origin reset tool for macs:
https://help.ea.com/en-us/help/origin/origin/how-to-reset-origin-on-mac/
Then download only the base game and install it. If you have the same issue as before, it might be better to take Origin out of the install process. Open a Finder window, then click Finder in the upper left corner of your screen, then Preferences. Under the Sidebar tab, make sure Hard discs is checked. You might need to close the Finder window and open another one to make the change stick.
On the left side of the window, click on the hard disk icon, then Library > Application Support > Origin > Download Cache. When you download a game from Origin, this is where the installer lands. Inside DownloadCache, you'll see a numbered folder, and inside that will be two files, one of which is a disc image (extension .dmg—you'll know it because it's very large, since it holds all the game files). You can drag the .dmg file onto your desktop and double-click it to run it, and your game should install without Origin's participation.
If you can't do this either, please make sure your mac has enough free storage. In the upper left corner of your screen, click on the Apple logo and select About This Mac. Then click the Storage tab to check.