Replace WordPress Search With Google Custom Search

I am trying to create a global search for a multisite website without having to use the sidebar or a plugin. I would like to replace the WordPress search with a Google Custom Search. I’ve tried to talk to others who have succeeded at this, but I am using a custom theme and it is making it extremely difficult to solve this. I am not really experienced in PHP, but I am trying to do the best I can.

search.php code:

<?php
$searchQuery = esc_attr($_GET['s']);
$postTypeQuery = get_query_var('post_type');
?>

<?php get_header(); ?>

<div class="wrapper wrapper_push">
    <!-- MAIN -->
    <div class="main" role="main">
        <div class="main-section">
            <div class="hdgBar">
                <h1 class="hdg hdg_h1">
                    <?php if ($searchQuery) : ?>
                        Search: <?php echo $searchQuery; ?>
                    <?php else : ?>
                        No Results Found
                    <?php endif; ?>
                </h1>
            </div>

            <div class="main-content">
                <div class="grid">
                    <!-- Post List -->
                    <div class="grid-col grid-col_9of12">
                        <?php if (!have_posts() || !$searchQuery) : ?>

                            <?php if ($searchQuery) : ?>
                                <p>No posts were found for that search term.</p>
                            <?php else : ?>
                                <p>Please enter terms to search for.</p>
                            <?php endif; ?>

                            <?php if ('post' !== $postTypeQuery && !is_home()) : ?>
                                <!-- Search -->
                                <fieldset class="searchSideBar" role="search">
                                    <form action="<?php bloginfo('home'); ?>/">
                                        <input type="input" name="s" placeholder="Search" class="input input_sidebar" />
                                        <?php if ('post' === $postTypeQuery || is_home()) : ?>
                                            <input type="hidden" value="post" name="post_type" id="post" />
                                        <?php endif; ?>
                                        <input type="submit" class="search-mag search-mag_red" value=""/>
                                    </form>
                                </fieldset>
                            <?php endif; ?>
                        <?php else : ?>
                        <ul class="mediaGroup">
                            <?php
                            $i = 0;
                            ?>
                            <?php if (have_posts()) : while (have_posts()) : the_post(); $i++; ?>
                                <?php ($i > 5) ? $class = ' hidden' : $class = ''; ?>
                                    <li class="postList-item<?php echo $class; ?>">
                                        <div class="media">
                                            <div class="media-img">
                                                <?php if (has_post_thumbnail()) : ?>
                                                    <a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>">
                                                        <?php the_post_thumbnail('120x120'); ?>
                                                    </a>
                                                <?php else : ?>
                                                <div class="placeholder placeholder_categoryListItem">
                                                    <a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>">
                                                        <img class="placeholder-img_categoryListItem" src="<?php echo THEME_PATH_URL; ?>/assets/images/placeholder-logo.png" />
                                                    </a>
                                                </div>
                                                <?php endif; ?>
                                            </div>
                                            <div class="media-bd media-bd_inline">
                                                <div class="fullView">
                                                    <?php
                                                    $cats = wp_get_post_categories(get_the_ID());
                                                    ?>

                                                    <?php if (count($cats)) : ?>
                                                        <ul class="tag tag_push">
                                                            <?php foreach ($cats as $catId) : ?>
                                                                <?php
                                                                $category = get_category($catId);
                                                                ?>
                                                                <li>
                                                                    <a href="<?php echo get_category_link($category->cat_ID); ?>" class="tag-link">
                                                                        <?php echo $category->name; ?>
                                                                    </a>
                                                                </li>
                                                            <?php endforeach; ?>
                                                        </ul>
                                                    <?php endif; ?>
                                                </div>
                                                <div class="hdgBar hdgBar_thin">
                                                    <h2 class="hdg hdg_h2">
                                                        <a href="<?php the_permalink(); ?>" class="hdg hdg_h2">
                                                            <?php the_title(); ?>
                                                        </a>
                                                    </h2>
                                                </div>
                                                <div class="fullView">
                                                    <?php
                                                    $excerpt = get_the_excerpt();
                                                    if (strlen($excerpt) > 180) {
                                                        $excerpt = substr($excerpt, 0, 180) . '...';
                                                    }
                                                    echo $excerpt;
                                                    ?>
                                                </div>
                                            </div>
                                        </div>
                                    </li>
                            <?php endwhile;endif; ?>
                        </ul>
                        <div class="loadMore hidden">
                            <a href="#" class="btn btn_full">Load More</a>
                        </div>
                        <?php endif; ?>
                    </div>

                    <?php
                    if ($searchQuery && ('post' === $postTypeQuery || is_home())) {
                        get_template_part('views/sidebar', 'search');
                    }
                    ?>
                </div>
            </div>
        </div>
    </div>
</div>

<script>
    jQuery(document).ready(function($) {
        var $posts = $('.postList-item');
        var $loadMoreBtn = $('.loadMore');
        var postLimitIndex = 5;

        if ($posts.length > 5) {
            $loadMoreBtn.removeClass('hidden');
        }

        // Show more posts when load more btn clicked
        $loadMoreBtn.on('click', function(e) {
            e.preventDefault();
            postLimitIndex += 5;
            $posts
                .filter(function(index) {
                    if (index < postLimitIndex) {
                        if ($(this).hasClass('hidden')) {
                            return true;
                        }
                    }
                })
                .hide()
                .removeClass('hidden')
                .fadeIn(1500);

            if ($posts.length <= postLimitIndex) {
                $loadMoreBtn.hide();
            }
        });
    });
</script>

<?php get_footer(); ?>

The current search result page looks great, but I need to be able to include items from multiple sites within a WordPress multisite setup. I would like to keep the look the same, but show the results from all sites.

I created the google custom search, I have the ID and code but I do not know how to place it in the search.php in order to make it work correctly. Any suggestions would be extremely helpful.