I'm not familiar with Time Machine. Can you search its archive by file name? If so, look for files that match this pattern:

bookmarks-2014-01-08_4671.json

The date portion represents the date the backup was made, and the part after the date represents the number of bookmarks in the file.

By default, all of your Firefox data is in a hidden folder. If you need to explore Time Machine by folder, this article might help in figuring out how to do that: Profiles - Where Firefox stores your bookmarks, passwords and other user data.

You can restore the places.sqlite file to restore the bookmarks and the history.

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile

In Mac OS X v10.7 and later, the ~/Library folder is a hidden folder.

• http://kb.mozillazine.org/Show_hidden_files_and_folders#Mac_OS_X

• /Users/<user>/Library/Application Support/Firefox/Profiles/<profile>/