Display WP [gallery] shortcode, outside of the_content, on static front-page, then remove that shortcode from the_content on static front-page with a filter function attached to the_content filter

front-page.php

<?php
/**
 * A "Proof Of Concept" Front Page template that displays the first gallery found in the_content, above the_content.
 *
 * The concept could be applied to any singular template, single posts, single pages, single custom post types, static
 * front page, etc (not really for archive pages, or blog home). The function
 * yourthemeprefix_remove_first_gallery_shortcode will then remove the first gallery shortcode that it finds in the
 * content, from the front page, so that we only output the first one once, above our content, and not again, within
 * our content.
 *
 * @link    https://developer.wordpress.org/themes/basics/template-hierarchy/
 * @link    https://developer.wordpress.org/themes/template-files-section/page-template-files/page-templates/
 * @link    https://codex.wordpress.org/The_WordPress_Gallery
 * @link    https://codex.wordpress.org/Gallery_Shortcode
 * @link    https://codex.wordpress.org/Function_Reference/get_post_gallery
 * @link    https://codex.wordpress.org/Function_Reference/get_the_ID
 *
 * @package testing
 */

get_header(); ?>

<section class="row main-content-home" role="main">

	<?php while ( have_posts() ) : the_post(); ?>

		<?php if ( get_post_gallery( get_the_ID() ) ) : ?>
			<div class="gallery-display">
				<?php echo get_post_gallery( get_the_ID() ); ?>
			</div>
		<?php endif; ?>

		<div class="container">
			<h1><?php the_title(); ?></h1>
			<?php the_content(); ?>
		</div>

	<?php endwhile; ?>

</section>

<?php get_sidebar(); ?>

<?php

get_footer();

functions.php

<?php
/**
 * Your Theme's functions.php file.
 */

/**
 * Remove the first [gallery] shortcode from the_content of static front page's main query.
 *
 * Returns early wherever possible.
 * This is intentionally written to be very overly ridiculously verbose, for ease of study.
 * This function is fired on the_content filter, with a priority of 10.
 * Be aware that if it were to fire later, say priority 11, do_shortcode would have already run, and the shortcode
 * we are looking to remove would no longer be in the $content string.
 *
 * @filter the_content priority 10
 *
 * @link   https://pippinsplugins.com/playing-nice-with-the-content-filter/
 * @link   https://developer.wordpress.org/reference/functions/is_main_query/
 * @link   https://developer.wordpress.org/reference/functions/is_front_page/
 * @link   https://developer.wordpress.org/reference/functions/is_home/
 * @link   https://codex.wordpress.org/Function_Reference/is_home#Blog_Posts_Index_vs._Site_Front_Page
 * @link   http://php.net/manual/en/function.strpos.php
 * @link   https://developer.wordpress.org/reference/functions/get_shortcode_regex/
 * @link   http://php.net/manual/en/function.preg-match-all.php
 * @link   http://php.net/manual/en/function.array-search.php
 * @link   http://php.net/manual/en/function.str-replace.php
 * @link   https://github.com/WordPress/WordPress/blob/4.3-branch/wp-includes/default-filters.php#L388
 *
 * @param string $content Content of the current post.
 *
 * @return  string
 */
function yourthemeprefix_remove_first_gallery_shortcode( $content = null ) {

	/**
	 * If there's no content, return early. Presumably the content would never be empty, but it's better to be safe than
	 * make assumptions and throw warnings and errors later.
	 */
	if ( empty( $content ) ) {
		return $content;
	}

	/**
	 * If this is not the main query, return early.
	 */
	if ( ! is_main_query() ) {
		return $content;
	}

	/**
	 * If this is not the front page (what most people would call "homepage"), return early.
	 */
	if ( ! is_front_page() ) {
		return $content;
	}

	/**
	 * If this is the front page, but front page is a blog listing (not a static page), return early.
	 */
	if ( is_home() ) {
		return $content;
	}

	/**
	 * Locate position of the string '[gallery' relative to the beginning of the content string.
	 *
	 * Note that string positions start at 0, and not 1. Returns FALSE if '[gallery' needle was not found.
	 * Use strict === equality to evaluate position (in case position was found at 0). This is a faster "check" than
	 * preg_match, which is why I'm calling it before we ever get to preg_match. We want to avoid heavy processing
	 * wherever possible, and return early wherever possible, so we do not have a detrimental impact on performance.
	 * If we didn't find the position of '[gallery' then the shortcode is not in the content, and we can return early,
	 * avoiding further, unnecessary processing.
	 *
	 * @var bool|int $position
	 */
	$position = strpos( $content, '[gallery' );

	/**
	 * If there's no gallery position in content, return early.
	 */
	if ( false === $position ) {
		return $content;
	}

	/**
	 * Get the shortcode search regular expression pattern.
	 *
	 * @var string $shortcode_regex
	 */
	$shortcode_regex = get_shortcode_regex();

	/**
	 * If there's no shortcode regular expression pattern, return early. I can't imagine this ever being empty, but it's
	 * better to be safe than make assumptions and throw warnings and errors later.
	 */
	if ( empty( $shortcode_regex ) ) {
		return $content;
	}

	/**
	 * Fill the $matches array with shortcodes found in the content.
	 * Depending on what's in your content, it could look something like this.
	 *
	 *      $matches = Array
	 *      (
	 *          [0] => Array
	 *              (
	 *                  [0] => [video mp4="http://site.com/wp-content/uploads/2015/09/movie.mp4"][/video]
	 *                  [1] => [gallery link="none" columns="1" size="full" ids="202,3378,3376" orderby="rand"]
	 *              )
	 *          [1] => Array
	 *              (
	 *                  [0] =>
	 *                  [1] =>
	 *              )
	 *          [2] => Array
	 *              (
	 *                  [0] => video
	 *                  [1] => gallery
	 *              )
	 *          [3] => Array
	 *              (
	 *                  [0] =>  mp4="http://site.com/wp-content/uploads/2015/09/movie.mp4"
	 *                  [1] =>  link="none" columns="1" size="full" ids="202,3378,3376" orderby="rand"
	 *              )
	 *          [4] => Array
	 *              (
	 *                  [0] =>
	 *                  [1] =>
	 *              )
	 *          [5] => Array
	 *              (
	 *                  [0] =>
	 *                  [1] =>
	 *              )
	 *          [6] => Array
	 *              (
	 *                  [0] =>
	 *                  [1] =>
	 *              )
	 *      )
	 */
	preg_match_all( '/' . $shortcode_regex . '/s', $content, $matches );

	/**
	 * Matches[2] is empty, return early.
	 */
	if ( empty( $matches[2] ) ) {
		return $content;
	}

	/**
	 * Find the first occurrence of the string 'gallery' in the $matches[2] array.
	 *
	 * @var int $key
	 */
	$gallery_key = array_search( 'gallery', $matches[2] );

	/**
	 * The array search did not locate the string 'gallery', return early.
	 * Theoretically this shouldn't happen, based on the checks we had earlier, but better to be safe than make
	 * assumptions and throw errors and warnings.
	 */
	if ( false === $gallery_key ) {
		return $content;
	}

	/**
	 * Find the first gallery shortcode string in the $matches[0] array, that corresponds to the $gallery_key found by
	 * array_search.
	 *
	 * @var string $first_gallery_shortcode
	 */
	$first_gallery_shortcode = $matches[0][ $gallery_key ];

	/**
	 * Amazingly, we don't have a matching shortcode string, return early.
	 * Theoretically this shouldn't happen, based on the checks we had earlier, but better to be safe than make
	 * assumptions and throw errors and warnings.
	 */
	if ( empty( $first_gallery_shortcode ) ) {
		return $content;
	}

	/**
	 * We have the very first gallery shortcode from the content, strip it out, because we already displayed it in the
	 * front-page.php template, outside of the content.
	 */
	$content = str_replace( $first_gallery_shortcode, '', $content );

	return $content;
}

add_filter( 'the_content', 'yourthemeprefix_remove_first_gallery_shortcode', 10 );