Hiding by default posts in given category except for some cases

wpse276485_exclude_archived($query) {
  if ( !is_admin() && !is_category('archived') ) {
    $query->set('category__not_in', array(get_cat_ID('archived')));
  }
}

add_action('pre_get_posts','wpse276485_exclude_archived');

That should do it, assuming the name of your category is “archived”.

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