index.js

'use strict'

const express = require('express')
const app = express()

app.get('/', (req, res) => {
  res.send('index')
})

app.get('/foo', (req, res) => {
  res.send('foo')
})

app.get('/bar', (req, res) => {
  res.send('bar')
})

module.exports.handler = (req, res) => {
  if (req.url === '') {
    req.url = '/'
  }

  app.handle(req, res)
}

package.json

{
  "dependencies": {
    "express": "^4.16.2"
  }
}

❯ curl https://redacted.cloudfunctions.net/hello-world
index

❯ curl https://redacted.cloudfunctions.net/hello-world/
index

❯ curl https://redacted.cloudfunctions.net/hello-world/foo
foo

❯ curl https://redacted.cloudfunctions.net/hello-world/bar
bar