If you click on the New Threads link to see what threads have new posts, at least you get the ones with the latest updates. But no, the search results don't show the date of when the thread was started. The only options we have is either to click on the first page of a thread to see when it started or, if doing an Advanced Search for a specific keyword or tag, you can sort results by Thread Start Date to see which ones have the oldest beginnings. But threads that are "ancient" can still be quite relevant.
Also, there are long-running still-active threads here that were started ages ago, and which had some long breaks in postings, and are still popular, such as the Tattoos thread
. That was started in July 2009 and was posted to as recently as Jan. 2013.