How to make WP_Query faster when getting a post from one year ago?

Try below code. It will improve performance. First of all you have used below argument inside date_query instead of outside of date_query. It should be corrected.

1. post_parent
2. post_status
3. orderby
4. order
5. column – it isn’t required. so removed.

I have removed before and instead used year, month, day.

References :
WP_Query &
WP_Date_Query

<?php 
 // Get the date for one year ago
 $one_year_ago = date('Y-m-d', strtotime('-1 year'));

 // Set up the WP_Query
 $args = array(
      'post_type' => 'post',  // Can be changed to another post type if needed
      'posts_per_page' => 1,      // Number of posts to retrieve, -1 for all
      'post_parent' => '',
      'post_status' => 'publish',
      'orderby' => 'date',
      'order' => 'DESC',
      'date_query' => array(
            array(
                'year'  => date('Y', strtotime($one_year_ago)),
                'month' => date('m', strtotime($one_year_ago)),
                'day'   => date('d', strtotime($one_year_ago)),
            ),
       ),
 );
 
 $query = new WP_Query( $args ); 

 while($query->have_posts()) : $query->the_post(); 
 ?>
    <a href="<?php the_permalink() ?>">
    <?php the_title(); ?></a>
 <?php endwhile; wp_reset_postdata();?>