woocommerce_new_product action doesn’t fire

Try like

function add_this_to_new_products( $new_status, $old_status, $post ) {
    global $post;
    if ( $post->post_type !== 'product' ) return;
    if ( 'publish' !== $new_status or 'publish' === $old_status ) return;
    add_post_meta( $post->ID, 'total_amount', '0', true ); // This is the action to take
}

add_action( 'transition_post_status', 'add_this_to_new_products', 10, 3 );