I want to cache cloud function data in to cdn. Whatever i tried is caching in browser only

I have a webpage application developed using Flutter.
I am hosting this on Firebase hosting.
There are some data which changes over a long period of time say in 2-3 days. So I am fetching this data through Firebase cloud function.

Is there any way the data sent by the cloud function get cached to cdn? The steps that i tried so far, are caching in the browser only.

Here is firebase.json

{
  "hosting": {
    "target": "flutter",
    "public": "build/web",
    "headers": [
      {
        "source": "**",
        "headers": [
          {
            "key": "Cache-Control",
            "value": "'public, max-age=300, s-maxage=600'"
          }
        ]
      }
    ],
    "ignore": [
      "firebase.json",
      "**/.*",
      "**/node_modules/**"
    ],
    "rewrites": [
      {
        "source": "**",
        "destination": "/index.html"
      },
      {
        "source": "/fetchData/**",
        "destination": "/index.html"
      }
    ]
  }
}

and here is my cloud function

var globalData = "some global static data"
const functions = require("firebase-functions");

const cors = require("cors");

exports.fetchData = functions.https.onRequest(async (req, res) => {
  var corsFn = cors();

  await corsFn(req, res, async function () {
    var body = req.body;


    res.set("Cache-Control", "public, max-age=300, s-maxage=600");

    res.status(201).send({
      data: globalData,
    });
  });
});

with this, I am able to cache the cloud function data but only in the browser. What I want is to cache in Firebase global cdn.