How to get all post titles starting with numbers and symbols?

Hook into the posts_where filter and add your condition to the query:

add_filter('posts_where', function($where){
  global $wpdb;
  return "{$where} AND {$wpdb->posts}.post_title REGEXP '^[0-9\$\@\!\?\%]'";
                                // add other symbols in the regex above ^
});

Then do your query:

$my_query = new WP_Query(...);

You may want to remove the filter after you get the results (make it a normal function so you can pass the name to remove_filter).