Psychosopher,
To make widgets collapsed initially, you have to add some CSS code. For example, following is the CSS to make widgets collapsed except Recent Posts in TwentyFourteen’s left sidebar.
#primary-sidebar .widget h1+* {
display: none;
}
#primary-sidebar .widget_recent_entries h1+* {
display: block;
}
All widgets in the sidebar will be collapsed by the first CSS block. And the Recent Posts widget will be uncollapsed by the second.
This is just a concept and you might have to adjust code to your theme. When you find it difficult, I will help you if you can show me your site.
After a few weeks of no response, I’d like to mark this as resolved because I’ve answered enough information.