Just remember, the route prefix you use to define the CloudFront behavior will also be added to the request sent to the origin server. So in this case, all routes defined by the API must be prefixed with `/api/`. This makes it hard to refactor existing APIs with many routes and dependencies, but works great in a greenfield scenario.
(Of course, you can rewrite the URL on the fly via Lambda@Edge but that's a PITA to maintain)
(Of course, you can rewrite the URL on the fly via Lambda@Edge but that's a PITA to maintain)