Create sub single pages

First, you need to register the custom post type so that it has hierarchy, i.e. a post can have a parent post.

After that, you need to make sure your permalink structure is set to example.com/%postname%/.

Once you have that, you only need to create a child custom post named sub-single-slug and set single-slug as its parent from WordPress backend Editor’s Page Attribute (make sure it’s checked in Screen Options). That’s all. Now your sub-single-slug post will have the link structure as example.com/custom-post-type/single-slug/sub-single-slug/.

For example, I register the custom post type as follows:

function wpse_register_custom_post_type() {

    $labels = array(
        "name" => __( 'custom post type', 'text-domain' ),
        "singular_name" => __( 'custom post types', 'text-domain' ),
    );

    $args = array(
        "label" => __( 'custom post type', 'text-domain' ),
        "labels" => $labels,
        "description" => "",
        "public" => true,
        "publicly_queryable" => true,
        "show_ui" => true,
        "show_in_menu" => true,
        "capability_type" => "post",
        "map_meta_cap" => true,
        "hierarchical" => true,
        "rewrite" => array( "slug" => "custom_post_type", "with_front" => true ),
        "query_var" => true,
        "supports" => array( "title", "editor", "thumbnail", "custom-fields", "page-attributes" ),
        "taxonomies" => array( "category", "post_tag" ),
    );

    register_post_type( "custom_post_type", $args );
}

add_action( 'init', 'wpse_register_custom_post_type' );