Wordpress - 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.

You could simply use a "dummy" handle:

wp_register_style( 'dummy-handle', false );
wp_enqueue_style( 'dummy-handle' );

wp_add_inline_style( 'dummy-handle', '* { color: red; }' );

Your theme most certainly has a default stylesheet (otherwise it wouldn't it even be loaded as a theme). Just use this very stylesheet as the handler for your inline CSS. An example can be found in the functions.php of the theme TwentyFifteen (code skipped for brevity):

function twentyfifteen_scripts() {
    wp_enqueue_style( 'twentyfifteen-style', get_stylesheet_uri() );

}
function twentyfifteen_post_nav_background() {
    wp_add_inline_style( 'twentyfifteen-style', $css );
}