First off, this is a very attractive minimalist theme. Thank you for making it available.
How would I go about moving the navbar so it is positioned immediately underneath the carousel slider?
Move this code inside header.php
<div class="top-section">
<?php sparkling_featured_slider(); ?>
<?php sparkling_call_for_action(); ?>
</div>
From very bottom of that file all way up above
<header id="masthead" class="site-header" role="banner">
Some other tweaks might be required but those are up to you.
This can be done via Child THeme as well by simply copy/pasting header.php file to Child Theme and then do necessary changes.