The best way to shut out sound is in something called an anechoic chamber. This is a room completely covered in spiky triangular padding made of a certain material. None of the sound reflects off the walls so actually you can’t hear yourself. I’ve been in one and it’s weird not being able to hear your voice when you talk.
However, you still ‘hear’ the vibrations from your own body. To completely shut out ‘sound’ you would have to disconnect the ear from the brain, which happens to some people naturally (:() and I’m not sure if you would want to do it out of choice.
Your body is really really good at hearing things. It all goes back to our ancestors being able to protect themselves in the dark from wild animals…
Because your ears are so sensitive, if there is any motion of the molecules in the air that your brain can interpret as sound, it will. Even if you don’t use your ears to detect sound, the body can kind of pick up and interpret vibrations.
Unless you were really deaf, and the your ears became disconnected from your brain, you’d always be able to detect something.