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Here’s a snippet to make the post date into a link. This snippet only outputs a HTML5 post date, if you need an XHTML version just edit the $new_output variable.

add_filter( 'genesis_post_meta', 'child_post_meta_filter' );
function child_post_meta_filter($post_meta) {
	if ( !is_page() ) {
		$post_meta = '[post_categories before=""] [post_date]';
	}
	return $post_meta;
}

//* Add permalink to [post_date] shortcode
add_filter( 'genesis_post_date_shortcode', 'child_customize_post_date_shortcode', 10, 2 );
function child_customize_post_date_shortcode( $output, $atts ) {

	global $post;
	$defaults = array(
		'after'  => '',
		'before' => '',
		'format' => get_option( 'date_format' ),
		'label'  => '',
	);

	$atts = shortcode_atts( $defaults, $atts, 'post_date' );
		
	$display = ( 'relative' === $atts['format'] ) ? genesis_human_time_diff( get_the_time( 'U' ), current_time( 'timestamp' ) ) . ' ' . __( 'ago', 'genesis' ) : get_the_time( $atts['format'] );
	
	$new_output = sprintf( '<time %s>', genesis_attr( 'entry-time' ) ) . '<a rel="bookmark" href="' . get_permalink() . '">' . $display . '</a>' . '</time>';
	
	return $new_output;
}

Thanks Gary Jones for help with the filter!