Hello Justin,
Currently there is not setting to do so. You can however manually hack the code to keep the story box open when the page is first loaded. Go to your /components/com_easysocial/themes/wireframe/story/default.php and located the following html code at line 14:
<div class="es-story es-responsive is-collapsed" data-story="<?php echo $story->id;?>" data-story-form data-story-hashtags="<?php echo implode(',', $story->hashtags); ?>">
// Replace it with
<div class="es-story es-responsive is-expanded" data-story="<?php echo $story->id;?>" data-story-form data-story-hashtags="<?php echo implode(',', $story->hashtags); ?>">
Hope these help.