Hi @pyecrust
The space you see is comming from header.php file.
If you need nothing in this header section remove or you can comment those bit of shown below:
<header id="masthead" class="site-header" role="banner">
<div class="site-header-main">
<div class="site-branding">
<?php if ( is_front_page() && is_home() ) : ?>
<h1 class="site-title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></h1>
<?php else : ?>
<p class="site-title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></p>
<?php endif;
$description = get_bloginfo( 'description', 'display' );
if ( $description || is_customize_preview() ) : ?>
<p class="site-description"><?php echo $description; ?></p>
<?php endif; ?>
</div><!-- .site-branding -->
<?php if ( has_nav_menu( 'primary' ) || has_nav_menu( 'social' ) ) : ?>
<button id="menu-toggle" class="menu-toggle"><?php _e( 'Menu', 'twentysixteen' ); ?></button>
<div id="site-header-menu" class="site-header-menu">
<?php if ( has_nav_menu( 'primary' ) ) : ?>
<nav id="site-navigation" class="main-navigation" role="navigation" aria-label="<?php _e( 'Primary Menu', 'twentysixteen' ); ?>">
<?php
wp_nav_menu( array(
'theme_location' => 'primary',
'menu_class' => 'primary-menu',
) );
?>
</nav><!-- .main-navigation -->
<?php endif; ?>
<?php if ( has_nav_menu( 'social' ) ) : ?>
<nav id="social-navigation" class="social-navigation" role="navigation" aria-label="<?php _e( 'Social Links Menu', 'twentysixteen' ); ?>">
<?php
wp_nav_menu( array(
'theme_location' => 'social',
'menu_class' => 'social-links-menu',
'depth' => 1,
'link_before' => '<span class="screen-reader-text">',
'link_after' => '</span>',
) );
?>
</nav><!-- .social-navigation -->
<?php endif; ?>
</div><!-- .site-header-menu -->
<?php endif; ?>
</div><!-- .site-header-main -->
<?php if ( get_header_image() ) : ?>
<?php
/**
* Filter the default twentysixteen custom header sizes attribute.
*
* @since Twenty Sixteen 1.0
*
* @param string $custom_header_sizes sizes attribute
* for Custom Header. Default '(max-width: 709px) 85vw,
* (max-width: 909px) 81vw, (max-width: 1362px) 88vw, 1200px'.
*/
$custom_header_sizes = apply_filters( 'twentysixteen_custom_header_sizes', '(max-width: 709px) 85vw, (max-width: 909px) 81vw, (max-width: 1362px) 88vw, 1200px' );
?>
<div class="header-image">
<a href="<?php echo esc_url( home_url( '/' ) ); ?>" rel="home">
<img src="<?php header_image(); ?>" srcset="<?php echo esc_attr( wp_get_attachment_image_srcset( get_custom_header()->attachment_id ) ); ?>" sizes="<?php echo esc_attr( $custom_header_sizes ); ?>" width="<?php echo esc_attr( get_custom_header()->width ); ?>" height="<?php echo esc_attr( get_custom_header()->height ); ?>" alt="<?php echo esc_attr( get_bloginfo( 'name', 'display' ) ); ?>">
</a>
</div>
<?php endif; // End header image check. ?>
</header><!-- .site-header -->
Remember removing this code not only effect the header your menus and other section might not work.
So you can look properly and remove what you don’t want.
Best Regards!!