JZ,
Since Firebase Cloud Messaging is by definition a cloud product, as is the rest of Firebase, I don't think this is possible.
To be honest, as a somewhat naïve cloud developer ,I'm not even sure how one would go about reaching any server without touching any other ISPs, backbone providers, or internet services (Call it up with a dialup modem, maybe? But I'm fairly sure even then it's going to hit some carrier services along the way).
Or did you have specific, detailed constraints on what you mean by "not self-hosted"?
☼, Kato