AWS lambda + API gateway. I use serverless to deploy to these.

If traffic is high, this could get pricy. For example, i have a site up getting about 20,000k visitors a day, hitting it many times each and it's probably costing me $400/month whereas a $50 server would probably do the trick (it's a temporary thing that i'm migrating away soon). But I have a bunch of smaller projects with a few visitors a day and the cost rounds to $0.

The nice thing is that it'll basically scale infinitely when you need it to.