Convert all dates in field to Unix time, except those already in Unix time

strtotime is php function that can be used for this purpose.
strtotime — Parse about any English textual datetime description into a Unix timestamp

1. Firstly get all the posts using meta key .
2. Then get date value from meta field.
3. Then convert to unix timestamp.
4. Then update again.

$args = array( 'posts_per_page' => -1, 'meta_key' => 'meta_key_name' );

$myposts = get_posts( $args );
foreach ( $myposts as $post ) : setup_postdata( $post ); 
         $date = get_post_meta(get_the_id(), 'meta_key_name', true);

         if( strtotime($date) != false ){ // To exclude dates which are already in timestamp
            update_post_meta(get_the_id(), 'meta_key_name', strtotime($date));
          }
    endforeach; 
wp_reset_postdata();?>