Thanks @Patryk, your comment helped me to think about one more step.

I am using Firestore as a database. During the firebase init hosting you need to change default settings.

ng build --configuration development
...
firebase init hosting
...
Configure as a single-page app (rewrite all urls to /index.html)?

Simplest way of solving the isse was to answer Yes to the above question during init.

Once I've answered "Y" firebase.json got updated with:

"rewrites": [
      {
        "source": "**",
        "destination": "/index.html"
      }
    ]

and it fixed the issue.