How do I hide the entire parent (top) level in superfish? Using the Superfish module, I need to show just the second level and below. That means, hide the entire first (parent) level and only show the child level based on the current page.

Is this possible?

I tried editing the Superfish block and changing the menu depth, but it doesn't allow me to choose the depth to exclude above it.
Menu block module allows you to choose which level to show, and how deep.

It won't integrate with superfish module, but allows you to build the submenus you're looking for. Moreover, those submenus may be themed to use basic superfish:

function THEMENAME_menu_tree__menu_block__1($variables) {
    return '&lt;ul class="menu sf-menu"&gt;'. $variables['tree'] .'&lt;/ul&gt;';
}


1 in the function name is the delta of the custom menu_block created.

Although posible, there's no straight way to leverage advanced superfish configuration / styling within a menu_block: APIs are not isolated enough as to theme a menu_block with a complex superfish style in a few of lines.

Just note also that a closer integration of both modules is feasible (I think of superfish using menu_block API).

So, although incomplete, I think menu_block + superfish is the best alternative.