What do you mean restore files from my Mac Time machine? In Windows I use there is such a option like that but doing so shouldn't cause install issues your having. I think something else is going on here.

What files did you restore from the Time Machine backup? The normal/best procedure for a profile missing error is to create a new profile if you can't recover by registering an existing profile. *https://support.mozilla.org/en-US/kb/how-run-firefox-when-profile-missing-inaccessible You can create a new profile as a quick test to see if your current profile is causing the problem. See "Creating a profile": *https://support.mozilla.org/en-US/kb/profile-manager-create-remove-switch-firefox-profiles If the new profile works, you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems. *https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile