I'm using [s2Member-List-Search-Box /] together with [s2Member-List /]. After I press search it displays search results. Is there a way to suppress the list unless and until a search is performed?

Yes, you could use a conditional for this.

  1. Install the ezPHP plugin for WordPress. See: https://wordpress.org/plugins/ezphp/
  2. Use the Text tab in your WordPress editor and add the following conditional PHP tags.
[s2Member-List-Search-Box /]

<?php if(!empty($_REQUEST['s2-s'])): ?>
    [s2Member-List enable_list_search="yes" /]
<?php endif; ?>