Community members and experts generally advise against trying to find old trial keys due to security and activation hurdles.
Since Office 2010 is obsolete and potentially unsafe, consider these modern options: Office 2010 free trial key
Microsoft ceased distributing trial versions of Office 2010 shortly after the release of Office 2013 and Office 365. Critical Review of Online "Free Keys" purchased product key
When searching for "free trial keys" today, you will likely encounter third-party blogs or forums offering lists of keys. you cannot officially install the software.
Official download links have been retired. If you do not already have the installation media (CD or backup file) and a original, purchased product key, you cannot officially install the software.