A 2003 Google patent, "Information retrieval based on historical data" (US 7,346,839), describes scoring a document by its "inception date", possibly the date its domain was registered. A patent shows what Google invented, not what it runs, and no Search Central 1 page lists domain age: it is unconfirmed. Age mostly stands in for the content and links a site has had time to earn.
Buying an old domain for its history can backfire: Google's expired domain abuse policy targets expired domains "repurposed primarily to manipulate search rankings". Check a used domain's past in the Wayback Machine 146 (web.archive.org (https://web.archive.org/ 146 )) first.