You can hook into the loading of any admin screen with
add_action( 'load-post.php', 'tbdn_post_screen' );
function tbdn_post_screen() {
// Check here whether you're adding a post or
// editing a post by seeing if $_GET['action']
// equals 'edit' then add your meta for post with
// ID $_GET['post']
}
Details of all of the admin screen load- hook values are at https://codex.wordpress.org/Plugin_API/Admin_Screen_Reference