Does the Console app in macOS keep a log of when I deleted a certain file?
No. The filesystem doesn’t directly or indirectly to the console have a journal or log of changes in files or folders or permissions. 

There are some tools to do that, but none ship enabled or configured with the os. 

Time Machine is the way to find when the file was last present and it’s searchable from spotlight. 

I would set that up now or connect and get a current backup before you do any troubleshooting so if you need to erase the drive or repair it, your other files are covered at least now and going forward.