I think that what you want is have all topics that are pulled to Discourse from your website be marked as unlisted. When a topic receives a comment, it would automatically be marked as listed. Unlisted topics do not appear in the topic list, so this would prevent the topic list on your site from being full of topics with no responses.
This type of configuration makes sense for sites where people are accessing Discourse topics by clicking a “Start Discussion” link that is displayed below a blog post. Discourse does not have a setting for this, but I think it would be a reasonable feature request. The DIscourse WordPress plugin has this functionality, but it uses the Discourse API for unlisting and listing the topics.