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@24898cb1433bdf3a  With a base game disc manufactured prior to September 2012, you should be able to start the install process and simply decline the offer to let the EA Download Manager handle the installation.  The EADM will try to "update" itself to Origin, but if it's not a part of the process, that never happens.

Please make sure when installing Sims 3 that Origin and the EA App are NOT currently installed on your computer; if they are, remove them with Revo Uninstaller (the free version is fine).  If you have a previous Sims 3 installation, remove that with Revo as well.  If Revo doesn't find anything, use Piriform's CCleaner (again, the free version is fine) to look for Sims 3-related data and remove that.

Install the base game, decline the EADM's offer to manage the install process, and you should be able to play without Origin or the EA App.  If the base game works, install your packs one at a time and in order of release, for example World Adventures would be the first one to install.  Each time, launch the game to make sure it still works.  After installing Generations, use the Super Patch to manually patch the game to 1.67.  You can find it here, under "Cumulative Base Game Super Patcher":

https://forums.thesims.com/en_US/discussion/175477/official-ea-download-link-for-the-sims-3-cumulative-manual-update

After that, you can install your remaining packs in any order—either starting with Generations or the next pack released, patches were incorporated into the base game rather than the individual packs.  Run the Super Patch again after your last pack is installed.

And just to clarify, it doesn't matter when the discs for your packs were manufactured, only the base game.  The packs' discs don't or at least shouldn't require Origin no matter how new they are.