Cloud Functions supports OAuth 2.0 user authorization out of the box and you can bound your App ID instance directly to it.
Here's a fairly recent tutorial showing the steps:
https://www.ibm.com/cloud/blog/authenticating-users-with-cloud-functions-api-gateway-and-app-id
If you're looking to automatically initiate a new authentication flow as in redirect to the an identity provider where you're user will sign in, you'll have to either add logic to your application using an OIDC SDK (For instance App ID's: https://github.com/ibm-cloud-security/appid-serversdk-nodejs/) or add it manually handle the flow from a set of actions.
If you go the action approach, you'll have to keep in mind that they are ephemeral and can't keep session state, so you'll have to keep secure cookies in the user's browser.