Angular Proxy in root level

I have an Angular application and a landing page written in jQuery.

I want to serve the landing page every time the request is on the root of http://mywebsite.com. Anything else, let's say http://mywebsite.com/otherpage, I want to serve the Angular application.

With nginx (production), this is fairly easy.

When developing Angular, we can easily proxy other requests, like /api, with --proxy-config proxy.config.json CLI option.

The problem I'm getting is with the root level.

What am I doing wrong? Can't I proxy the root level?

Angular docs tells us to go to Webpack dev-server docs, but still I couldn't figure out how to do it.

My proxy.config.json is like the following:

{
  "/api/*": {
    "target": "http://localhost:3000",
    "secure": false,
    "logLevel": "debug"
  },
  "/": {
    "index": "",
    "target": "http://localhost:3000",
    "secure": false,
    "logLevel": "debug"
  }
}

from Angular Proxy in root level