First, ensure that you have API access enabled on your Rocket.Chat server. Navigate to the Rocket.Chat administration panel, and under the "REST API" settings, generate an authentication token. Note this token as it will be used to authenticate your API requests to extract data.

Use the Rocket.Chat REST API to fetch the data you need. For instance, to get messages or user information, make HTTP GET requests to the appropriate endpoints such as `/api/v1/channels.messages` or `/api/v1/users.list`. Use a tool like `curl` or a script in a language like Python or JavaScript to automate this data extraction process.

To upload data to Firestore, you need to use the Firebase Admin SDK. Install this SDK in your development environment. For Node.js, run `npm install firebase-admin`. For Python, use `pip install firebase-admin`. This SDK will facilitate communication with your Firestore database.

Create a new script to interact with Firestore. Import the Firebase Admin SDK and initialize it using your Firebase project credentials. You will need to download a service account key from the Firebase console and use it to authenticate your application. Follow the Firebase documentation to initialize the SDK with this key.

Once you've extracted the data from Rocket.Chat, you may need to transform it into a format that's suitable for Firestore. For example, Firestore typically stores data in JSON-like documents, so ensure your Rocket.Chat data adheres to this structure. This may involve converting timestamps, restructuring nested data, or renaming fields to match your Firestore schema.

With the Firebase Admin SDK initialized and your data formatted correctly, write a script to upload the data to Firestore. Use the SDK's methods to create or update documents in your Firestore database. Iterate over each piece of data from Rocket.Chat and use Firestore methods like `set()`, `add()`, or `update()` to insert the data into the appropriate collections and documents.

After uploading, verify that the data has been correctly transferred and is intact. Use the Firebase console to inspect the documents in your Firestore collections. Additionally, you can write scripts to randomly sample and compare specific entries between Rocket.Chat and Firestore to ensure the transfer was successful and all necessary data fields are correctly captured.

This guide provides a foundational approach to manually transferring data from Rocket.Chat to Firestore without using automated third-party solutions, focusing on direct API interaction and custom scripting.