How to show category list in WordPress

To limit the results to the children of the current product category, you can use parent parameter in get_terms(). The id of the current category, to be set as the parent value, will be get using get_queried_object().

$term_id = 0;
$queried_object = get_queried_object();
//
// check if it's a custom category
if ( $queried_object instanceof WP_Term )
    $term_id = $queried_object->term_id;

$args = array(
    'taxonomy'   => 'product_cat',
    'parent'     => $term_id,  // get only direct children
    //'child_of' => $term_id,  // get all children 
    //'hide_empty' => false,
);
$terms = get_terms( $args );

If you would like to attach the current category to the results (before the child categories):

$terms = get_terms( $args );
if ($queried_object instanceof WP_Term) {
    array_unshift( $terms, $queried_object );
}

---

An example of the code in its entirety:

if ( is_archive('product') ) //  OR: is_product_category()
{
    $term_id = 0;
    $queried_object = get_queried_object();
    //
    // check if it's a custom category
    if ( $queried_object instanceof WP_Term )
        $term_id = $queried_object->term_id;

    $args = array(
        'taxonomy'   => 'product_cat',
        'parent'     => $term_id,  // get only direct children
        //'child_of' => $term_id,  // get all children 
        //'hide_empty' => false,
    );
    $terms = get_terms( $args );
    //
    // add current category at beginning
    if ($queried_object instanceof WP_Term) {
        array_unshift( $terms, $queried_object );
    }
    //
    // Check if any term exists and print them all
    if ( ! empty( $terms ) && is_array( $terms ) ) 
    {
        echo '<ul>';
        foreach ( $terms as $term ) { 
            printf('<li><a href="https://wordpress.stackexchange.com/questions/336877/%s">%s</a></li>',
                esc_url( get_term_link( $term ) ),
                $term->name
            );
        }
        echo '</ul>';
    }
}