Can the President end the Supreme Court by never nominating anyone?

The Supreme Court is a lifetime position, the President is 8 years max. Unless every single Justice and every single candidate for future Justice were to die, retire, or their nomination expire while a certain President were in office no. The Supreme Court would still function and new candidates would be nominated by the next President. Even if the President could some how impeach every single member (if he was successful with this, we failed as citizens) of the Supreme Court it would still function.