Begin by setting up a Google Cloud Project if you haven't already. Visit the [Google Cloud Console](https://console.cloud.google.com/), create a new project, and enable the Firestore API. This will allow you to use Firestore as your database.

Navigate to the `IAM & Admin` section in the Google Cloud Console. Create a new service account with the role of `Firestore Admin`. Download the JSON key file for this service account, which will be used to authenticate your application when accessing Firestore.

On the Apify platform, ensure your actor or task is set up correctly to scrape the desired data. Test your actor/task to confirm it is extracting the data accurately. Once verified, export the data in a format like JSON or CSV, accessible via Apify's dataset API.

On your local machine or server, set up a development environment. Install necessary libraries by running:
```bash
pip install google-cloud-firestore requests
```
These libraries will allow you to interact with Firestore and send HTTP requests to the Apify API.

Write a script to fetch data from Apify using their dataset API. Use the `requests` library in Python to make an HTTP GET request to the dataset URL, and parse the response to retrieve the data. Here's a basic example:
```python
import requests

response = requests.get('https://api.apify.com/v2/datasets/YOUR_DATASET_ID/items?format=json')
data = response.json()
```

Use the Firestore client library to authenticate and connect to your Firestore database. Load your service account JSON key and initialize the Firestore client:
```python
from google.cloud import firestore

# Use the path to your JSON key file
db = firestore.Client.from_service_account_json('path/to/your/service-account-key.json')
```

Iterate over your fetched data and insert each item into Firestore. Create a new document for each data entry and specify the collection where you want to store your data:
```python
for item in data:
db.collection('your_collection_name').add(item)
```
Ensure that your data structure in Firestore aligns with the data you are transferring.

By following these steps, you can effectively move data from Apify to Google Firestore without the use of third-party connectors or integrations. Adjust the script as necessary to handle specific data structures or additional logging/error handling as needed.