Change “No shipping method has been selected.…” from WooCommerce checkout notice

Solution:

This text is located in WC_Checkout Class inside validate_checkout() method. There are no filters to make changes to it, but you can use WordPress gettext filter for that as follows:

add_filter(  'gettext',  'change_checkout_no_shipping_method_text', 10, 3 );
function change_checkout_no_shipping_method_text( $translated_text, $text, $domain ) {
    if ( is_checkout() && ! is_wc_endpoint_url() ) {
        $original_text = 'No shipping method has been selected. Please double check your address, or contact us if you need any help.';
        $new_text      = 'Here your own text replacement.';
        
        if ( $text === $original_text ) {
            $translated_text = $new_text;
        }
    }
    return $translated_text;
}

Code goes in functions.php file of the active child theme (or active theme). Tested and works.