I wrote an article which proposes solutions to this problem: How to list all subcollections of a Cloud Firestore document? As a matter of fact, "retrieving a list of collections is not possible with the mobile/web client libraries" as explained in the Firestore documentation.

I would suggest you use the second method proposed in the article, using a Cloud Function.

Here is the code copied from the article.

Cloud Function:

const functions = require('firebase-functions');
const admin = require('firebase-admin');

admin.initializeApp();

exports.getSubCollections = functions.https.onCall(async (data, context) => {

    const docPath = data.docPath;

    const collections = await admin.firestore().doc(docPath).listCollections();
    const collectionIds = collections.map(col => col.id);

    return { collections: collectionIds };

});

Example of calling the Cloud Function from a web app:

  const getSubCollections = firebase
    .functions()
    .httpsCallable('getSubCollections');

  getSubCollections({ docPath: 'collectionId/documentId' })
    .then(function(result) {
      var collections = result.data.collections;
      console.log(collections);
    })
    .catch(function(error) {
      // Getting the Error details.
      var code = error.code;
      var message = error.message;
      var details = error.details;
      // ...
    });