My employer offers FaunaDB with a pay-per-request pricing model. To bypass cold-start lambda issues, I code the app to talk directly to the database. For certain richer functions I might invoke a Lambda, but for basic crud operations the database access control does the trick. And no cold-start issue.
Here's the data model part of my todo app if you want to see queries in the app: https://github.com/fauna/todomvc-fauna-spa/blob/master/src/T...