Insert static element only once in query archive

Use the Index of the post currently being displayed to trigger when your custom content is rendered.

current_post can be found on WP_Query from within the loop.

<?php while( $archive_query->have_posts() ) :

    $archive_query->the_post(); ?>

    <article <?php post_class(); ?>>
        The Content
    </article>

    <?php if ( $archive_query->current_post === 2 ): ?>

        <div>Custom Content</div>

    <?php endif; ?>

<?php endwhile; ?>