I think the impulse and personality have always existed. Link related is about a Victorian era proto-furry who made his own fursuits https://www.victorianvoices.net/ARTICLES/STRAND/1895B/S1895B-AnimalActor.pdf

There was apparently a theatrical culture of pantomime animals. From reading this article I definitely get the impression this guy would have been into Furry stuff if it had been available.