Create default text widget that displays default text

I have a theme with a custom widget area that I would like to default to containing a text widget pre-populated with some sample text (something like “here’s where you can put your intro text; go to the widgets panel to customize what this says”).

I know I want to emulate what sidebar.php does (declare some default widgets that are turned on when you activate the theme; adding anything via the widgets panel overrides these defaults). I tried just pasting in the code from sidebar.php: works fine, but that code is for widgets such as the archive one, not the text widget, leaving me stumped on how to add the sample text.

This page (https://codex.www.ads-software.com/Function_Reference/the_widget#Text_widget) says I should follow the format
<?php?the_widget('WP_Widget_Text',?$instance,?$args);??>

with default usage for the text widget looking like
<?php?the_widget('WP_Widget_Text');??>

so currently my header.php (where the customized widget area in question resides) includes this code:

<?php
	if ( ! dynamic_sidebar( 'about-text-widget' ) ) : ?>
			  <?php the_widget('WP_Widget_Text'); ?>
<?php endif; ?>

My PHP-n00b question is: how do I alter that code so that there isn’t only a default text widget appearing in my widget area, but a default text widget containing default text?

This is a child theme of Twenty Ten, by the way, though I believe the question is not theme-specific. Much thanks for any advice!