Show date as permalink for custom post type instead of post name

One thing you can do is pre-set the post_name field using the wp_insert_post_data hook. The field passes 2 variables: $data which is the initial default data and $postedarr which is what’s given whenever the post is $_POSTed, updated, or published.

/**
 * Modify the postdata before it's inserted into the database
 *
 * @param Array $data
 * @param Array $postarr
 *
 * @return void
 */
function wpse345850_modify_postdata( $data, $postarr ) {

    if( 'post' != $data['post_type'] || $postarr['ID'] ) {  // A $_POSTed ID means it's an update, not new
        return $data;
    }

    $data['post_name'] = date( 'Y-m-d' );

    return $data;

}
add_filter( 'wp_insert_post_data', 'wpse345850_modify_postdata', 10, 2 );

Note that you’ll have to change the above post type from post to your desired post type.