While working with documents, Excel temporary makes backups of opened files but when you close the software, the files get deleted and you only remain with the opened file. This is used for recovery in case there is a program crash.
TimeMachine was a good alternative to get back the previous edited files, but if it was disabled, then this option is eliminated.
Like in Windows, you can use an application which deals with file recovery which in this case I can recommend Wondershare Data Recovery. The software scans you drive for lost, deleted or broken files. Simply download and install the software and use the Lost File Recovery option and select DOCUMENTS as your starting point. If you know the file name, during search operation you will notice that all the recoverable files will be listed using the date as a sorting option. If you know the date when you modified the fileб you will have the ability to recover the file (if it's found).