You can create a Cloud Function with a public HTTP trigger to accomplish this.

The samples on that page include HTTP based Cloud Functions.

Here's the doc on calling http triggers.

To deploy a Cloud Function with an public HTTP trigger:

gcloud functions deploy MYFUNCTION --runtime <your runtime> --trigger-http --allow-unauthenticated

This command allows anonymous access to call your functions, ordinarily you would need to be authenticated to do so.

Once you open a trigger to the internet though anybody can call it so keep that in mind with what data you accept and pass back. You may also want to set a budget on the project containing the function in case somebody were to calling it continuously racking up a bill for you.

Cloud Functions for Firebase are a thin wrapper around Google Cloud Functions, so any approach that you can use for GCF (such as the one Jake proposes in their answer) also works on Firebase.

There are two ways to directly invoke a Cloud Function from within your application code with Firebase:

1. Create a HTTP endpoint and call that from your application code using something like fetch. This is described in the documentation on Call functions via HTTP requests
2. Implement a so-called Callable function in Firebase and then invoke that from your application code through the SDK. For more on this, see the documentation on Call functions from your app.

The second type essentially wraps the first type, but adds some features like named parameters, and it automatically passes the ID token and some other parameters.