Top level parent taxonomy ID

In general to get the posts of your custom post type you need to query post_type, if you want only the categories you could just pull the categories instead of the entire post type.

<?php query_posts(array( 'post_type' => 'CustomPostType' )); ?>
<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>

 <?php the_category(', '); ?>

<?php endwhile; else: ?>
<p>Sorry, no matches found.</p>
<?php endif; ?>

Or you could use get_terms()?
Quick example:

$terms = get_terms('CustomPostType');
foreach ( $terms as $term ) {
   echo $term->name.'<br />';
}

Are you listing anything else on that archive page? If you are for example listing posts (or other information) from the same post type you could combine it.

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EDIT:
I apologize I read over the comments in the script and thought you solely needed help with the rest. To just get the term id you could use get_terms() (as referred above). And then take a look at the following parameters:

 orderby (string)
    id
    count
    name - Default
    slug
    term_group
    none 

 order (string)
    ASC - Default
    DESC 

number (integer) 
    The maximum number of terms to return. Default is to return them all. 

fields (string)
    all - returns an array of term objects - Default
    ids - returns an array of integers
    names - returns an array of strings
    count - (3.2+) returns the number of terms found
    id=>parent - returns an associative array where the key is the term id and the value is the parent term id if present or 0 

Not including any other parameters it would look something like this:

$CustomPostType_ids = get_terms( 'CustomPostType', array(
    'orderby'    => 'id',
    'order'      => 'ASC',
    'number'     => 1,
    'fields'     => 'ids'
) );

You could also return all values and then just pull term_id.