It's much much older. As a kid growing up in NY in the 90s, I heard many times the version of this saying, "one cockroach on the floor means one hundred behind the wall."

That's different, though. The point of the ant thing is sometimes things just happen, but if they happen twice, that's a very different matter.

These sayings also causes needless panic over non-infesting cockroaches like ectobius pallidus that commonly wander inside by accident.