The Notes database is stored in ~/Library/Group Containers/group.com.apple.notes. You can find this in your Time Machine backups - I use Finder to do this.
If desperate try a) exit Notes, b) copy your existing ~/Library/Group Containers/group.com.apple.notes folder somewhere safe, c) guess a date when the note was present and find the folder in TM, d) copy the folder from Time Machine to ~/Library/Group Containers, e) run Notes, f) if that has worked, copy the contents of note you want to somewhere else. Then revert back to your current Notes by a) exit Notes, b) restore your safely preserved group.com.apple.notes back to ~/Library/Group Containers, and c) start Notes again.
This is messy and prone to all sorts of unexpected issues and mistakes (potential consequence is to lose all Notes) - I would only do it if really important to recover the lost note. As an additional precaution, I would export ALL existing notes from Notes to PDFs.
