Did anachronisms exist before movies/literature?
Yes. People can be anachroisms. An man who insisted on using Paleoloithic tools during the Neolithic on the grounds that flint scrapers were good enough for Grandad would have been an anachronsim. And given what I know of humanity I’m sure some caveman did just that.
How about someone whose username is part of a vaguely obscene '70s playground rhyme? 
Orally-transmitted myths and legends may well contain anachronisms, since they commonly accrete over time and could contain details that weren’t present at the initial event. The King Arthur mythos, for instance, contains mediaeval trappings when the core events were post-Roman.
Shakespeare is full of anachronisms. Likewise, what we can discover about how plays were staged in that era leads us to conclude that anachronism was the normal way to do things.