@jacqw9 There's no way for you to find the old account on your own if you don't know the email address tied to it. As for the discs themselves, you could install in Windows, but not in macOS, without needing access to the old account if, and only if, the base game disc was manufactured prior to September 2012. The newer discs require Origin, or now the EA App, to be present and managing the install process; the older ones do not. Check the fine print on the back for a copyright date, and the newer discs also have the Origin logo somewhere on the box.
It doesn't matter when the other discs were made; they should work without the EA App regardless. The one catch here is that you need to decline the EA Download Manager's offer to manage the install process for you, or else the EADM will attempt to update itself to Origin.
Your discs will of course not include the 64-bit Mac version. But even if your Mac supported 32-bit apps in general, 32-bit Sims 3 wouldn't work because all versions of macOS starting with El Capitan (2015 release) fail to authenticate these discs.
If you want to make one more attempt at finding the old account, EA customer support should be able to give you something like the first two characters plus the domain. You could ask your family members if anyone had ever had an email address that matched—it's possible you borrowed someone else's account at the time.
