Cannot exclude particular post from loop of custom post type

Something like this should work from your functions file as long as you use the correct conditional tag for your CPT archive:

function exclude_single_post_cpt($query) {
  if (is_post_type_archive('event') && $query->is_main_query() && !is_admin() ) {
    $query->set('post__not_in', array(1646));
  }
}

add_action('pre_get_posts', 'exclude_single_post_cpt');

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