This answer is fantastic, but in the interests of a minimal, runnable example I thought I'd share my complete code and workflow for getting up and running with a Puppeteer-based web app.
See this answer for a simple scheduler and a clock process version (although all three approaches can coexist in one app without doing anything special).
package.json:
{
  "name": "test-puppeteer",
  "version": "1.0.0",
  "description": "",
  "scripts": {
    "start": "node index.js"
  },
  "author": "",
  "license": "ISC",
  "dependencies": {
    "express": "^4.17.1",
    "puppeteer": "^9.1.1"
  }
}
Procfile:
web: node index.js
index.js:
const express = require("express");
const puppeteer = require("puppeteer");
const app = express();
app.set("port", process.env.PORT || 5000);
const browserP = puppeteer.launch({
  args: ["--no-sandbox", "--disable-setuid-sandbox"]
});
app.get("/", (req, res) => {
  // FIXME move to a worker task; see https://devcenter.heroku.com/articles/node-redis-workers
  let page;
  (async () => {
    page = await (await browserP).newPage();
    await page.setContent(`<p>web running at ${Date()}</p>`);
    res.send(await page.content());
  })()
    .catch(err => res.sendStatus(500))
    .finally(() => page.close())
  ;
});
app.listen(app.get("port"), () => 
  console.log("app running on port", app.get("port"))
);
Set up
- Install Heroku CLI and create a new app with Node and Puppeteer buildpacks (see this answer): - heroku create
heroku buildpacks:add --index 1 https://github.com/jontewks/puppeteer-heroku-buildpack -a cryptic-dawn-48835
heroku buildpacks:add --index 1 heroku/nodejs -a cryptic-dawn-48835
 - (replace - cryptic-dawn-48835with your app name)
 
- Deploy: - git init
git add .
git commit -m "initial commit"
heroku git:remote -a cryptic-dawn-48835
git push heroku master
 
- Verify that it worked with - curl https://cryptic-dawn-48835.herokuapp.com. You should see something like
 - <html><head></head><body><p>web running at Wed May 19 2021 02:12:48 GMT+0000 (Coordinated Universal Time)</p></body></html>