Yes. First, unregister the post type. (None of the actual data will be deleted if you already have posts.) Then, re-register it with
'rewrite' => array('slug' => 'page-name/custom-post-type-archive')
This will set your archive at the URL you’re looking for, and all the individual CPT posts will be “under” that – i.e. ‘/page-name/custom-post-type-archive/single-title/’.