What version do you have installed? Are you installing this on a new computer, having had it on a previous one? In that case, you don't need a product key. Just log into your Microsoft account, go to Services & subscriptions, and locate Product you've purchased. This should show Office 2016, and you can download from there.
If this is a newly purchased product, then it is almost certainly not legitimate since the current perpetual-license version of Office is Office 2021. Are you sure the message is not saying Office 2016 Professional Plus? If so, that is a volume license, not legal for individual use.