You certainly can do it with templates. Make a template that contains only {{date}}, then insert it into your document using the Templates menu, the “Insert template” command in the command palette, or Ctrl/Cmd T (if that’s the default hotkey and not one I set).
But you don’t need to, because there’s also an Insert date command in the command palette.
Unless you mean you want a date in your document that changes every time you open it. There may be a plugin way to do that, but I don’t know,
There is probably some JavaScript thing you could do, but I don’t know what.
But how would you? If the date changes every time you open the note, you’ll just see the current time, not the time you last worked on it.
If you want the date the note was last changed, there is a plugin for that (I don’t remember its name). Read the documentation, because if it uses the file system’s “last modified” date and you sync your vault, you might get inaccurate times.