There are a few ways to approach this. One way would be to have a Workflow that triggers on document creation. It could capture the relevant info (name, entry id) and send this information back. Maybe it could use a web request to their site. The site would save that and update the "latest document" page.

Or, a Workflow triggering on that same condition could be used to manage a folder of shortcuts to recently created documents. Then embedding Public Portal's browse.aspx to this folder would solve it.

Another approach is an SDK application that periodically runs a search for documents created since the last run, and reads the first result. It then updates a file that the web site reads.