There are couple of things you should check (btw, please share your the cloud function code snippet)
Make sure that you are calling/invoking supported GCP Vertex AI Gemini modes (Gemini 2.0, Gemini 2.5 Flash/pro etc.). Models like Palm, text-bison and even earlier Gemini models (like Gemini 1.0) has been deprecated, that's mostly likely the reason you are getting 404 reason due to model deprecation. Please check the supported model doc here to use a proper Gemini model.
Verify that you followed this Vertex AI getting started guide to set up your access to Gemini model. based on what you described:
You have GCP project
You enabled the Vertex AI API
IAM. Try to grant your GCP account Vertex AI User role permission. For detail, check Vertex AI IAM permission here.
I recommend to use Google Gen AI SDK for Python to call Gemini models. It handles the endpoint and authentication, you just need to code the model to use. for example: gemini-2.5-flash
These steps should get you going. Please share code snippet so that I can share the edited snippet back.