Using wp_add_inline_style without a stylesheet

You just need to add the styles directly to the page head. The best way to do this is to use the ‘wp_head’ action hook, assuming you are using a theme that has the hook. Like so:

add_action('wp_head', 'my_custom_styles', 100);

function my_custom_styles()
{
 echo "<style>*{color: red}</style>";
}

Check out the WP codex to learn more about action hooks.