It appears that Firebase can send push notifications. Firebase projects support Google service accounts which allow uploading the public key:
You can upload the public key portion of a user-managed key pair to associate it with a service account. After you upload the public key, you can use the private key from the key pair as a service account key.
However:
The key you upload must be an RSA public key that is wrapped in an X.509 v3 certificate and encoded in base64.
I don’t think Threshold ECDSA can help here. If such a thing as Threshold RSA were possible and implemented then it might provide a path forward.
Perhaps @JensGroth and @victorshoup can comment on that.