Use date in the URL of custom post type

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Custom post types can not use the “day/name” permalink structure defined in WordPress permalinks settings. You need to add your own rewrite rules to fit your needs.

For example:

add_action('init','my_rewrite_rules');
function my_rewrite_rules(){
    // Replace custom_post_type_slug with the slug of your custom post type
    add_rewrite_rule( 'custom_post_type_slug/([0-9]{4})/([0-9]{1,2})/([0-9]{1,2})/(.+)/?$', 'index.php?custom_post_type_slug='.$matches[4], 'top' );
}

Note that I’ve not tested the code above. You need to flush the rewrite rules before you test it.