WP Query Leads to 502 Bad Gateway (Timeout Because Query Takes Too Long)

It has nothing to do with WP_Query itself. The reason for such problem is what you do with this WP_Query. There’s no the_post() in your code, so the loop is infinite.

This is how to fix it:

 function bambam(){
     $args = array(
         'category_name' => 'breaking-news', 
         'post_date' => 'DESC',
         'posts_per_page' => 1
     );

     $the_query = new WP_Query( $args );

     if ( $the_query->have_posts() ) {
          echo '<div class="breaking-news">';
          while ( $the_query->have_posts() ) {
               $the_query->the_post();
              echo '<h1>' . get_the_title() . '</h1>';
          }
          echo '</div>';
          /* Restore original Post Data */
          wp_reset_postdata();
      } else {
          // no posts found
      }
}
bambam();