[thaumasiotes]

Here's a Wired article dated January 1, 2005 featuring the term "viral video" as something that doesn't need to be explained: https://www.wired.com/2005/01/check-out-this-video-clip/

So yes, we can be certain that "going viral" existed 20 years ago, to the extent that we think "viral" is the status achieved by "viral videos".