### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

We hit an incident where LiteLLM started returning Invalid model name for a model that was valid and configured (e.g. google/gemini-2.5-flash, but actually all 140 models that we've configured).

<img width="1864" height="647" alt="Image" src="https://github.com/user-attachments/assets/915d864f-d429-4f46-b258-d62e904e831b" />

This happened in a setup where LiteLLM uses a Postgres-backed config/state layer behind HAProxy. The leading pattern we observed is:

there is a transient Postgres / HAProxy instability a LiteLLM worker starts or refreshes during that instability the worker appears to miss its initial successful model/router load the worker still serves traffic all requests going through that worker fail with Invalid model name for otherwise valid models the issue stops after the worker is restarted or after a later successful refresh

What we expected to happen:

LiteLLM should not serve traffic until router/model state is successfully loaded at least once, or LiteLLM should keep retrying and recover automatically once Postgres connectiv…