How to hide empty ratings using Rate module?
How would people rate the item the very first time if the widget is hidden?

Look in Rate module's template folder for rate-template-fivestar.tpl.php. Copy it over into your theme's template folder then make changes.

I think the variable $count might be available (Number of votes), so you could print out a message if $count is 0 to say that the item has not yet been rated.