Not specifying z-index is the same as z-index: auto; that is its initial value.
auto and 0 mean the same thing if your element doesn’t create its own stacking context; e.g. it is not positioned as relative, absolute or fixed.
If your enclosing div isn’t positioned, then whatever you set its z-index to doesn’t matter; it and all its contents will participate in the stacking context of html, and its descendants will always be positioned in front of it.