Hola Carlos

This is a very good question and something that is often asked as it can be a bit confusing with the English translation using the verb "leave".

When we say with "Voy a salir de casa temprano" is literally "I'm going to get out of the house early" - with "get out of"  you can see the "de" in "de casa". However, the most natural translation in English is "leave the house" and this doesn't have any preposition. You'll very often see this with phrases like "salir de clase", salir de casa", "salir del trabajo". We don't use the most direct translation to "leave a place": dejar un lugar, because if we say "voy a dejar la casa" or "dejar el trabajo" it sounds as if you are "leaving something behind, forever".

I hope this helped clarify it.

Un saludo cordial

Inma