Ali called himself the Greatest Of All Time in the 1960s. There was plenty of exposure back in boomer days or Gen X.
But all this GOAT crap really didn't go haywire until after 2000 ... which is the era of millennials by named definition. Michael Jordan, LeBron, Messi, blah blah blah. None of them individual sport stars, mind you. Teams somehow don't matter in this calculus of stupid.
I don't know anybody over the age of 40 who voluntarily uses the term "GOAT" unless triggered to do so by someone in their 20s or 30s.