I know that Algolia can work perfectly fine with Firebase Realtime database but is there any way in which we can implement Algolia with Cloud Firestore using Android?
Syncing and indexing of data in Algolia are usually done in the backend (with Node.js for example). In the case of syncing Cloud Firestore and Algolia, you will need to use Firestore events in order to listen to new changes in Firestore and make the proper changes in Algolia (as described in their full-text search docs, which is in Node.js).
In order to search your data from Algolia in your Android app, you will need to use the Algolia mobile SDK that is written in Android (see Getting started for Android). If you want to query your Cloud Firestore, then you can separately use the Firebase SDK to achieve that.