• Open Automator and create a new Quick Action, search and double click to choose “Run AppleScript”, enter the following contents in the script editor area, and save it as “Launch iTerm”

  if application "iTerm" is running then
  	tell application "iTerm"
  		create window with default profile
  	end tell
  else
  	tell application "iTerm"
  		activate
  	end tell
  end if
  

• Set its shortcut in Keyboard → Shortcuts → services → General → Launch iTerm. Example: Command + Option + T

References

• https://superuser.com/a/1075548/735127
• https://iterm2.com/3.0/documentation-scripting.html
• https://apple.stackexchange.com/questions/175215/how-do-i-assign-a-keyboard-shortcut-to-an-applescript-i-wrote