Begin by visiting the TMDb website and creating an account if you haven't already. Once logged in, navigate to the API section to request an API key. This key will allow you to access TMDb's data programmatically. Store this key securely as it will be used to authenticate your requests.

Log in to the Google Cloud Console and create a new project. This project will house your Firestore database. Give your project a name and note the project ID, as you will need it for setting up Firestore and for authentication purposes.

Within your newly created Google Cloud project, navigate to the "Firestore" section under "Databases." Enable Firestore in Native mode for your project, which is optimized for mobile and web apps. This setup will allow you to store and manage your data with flexible querying capabilities.

On your local development environment, ensure you have Python installed. Install the required libraries using pip. You will need libraries like `requests` for API calls and `google-cloud-firestore` for interacting with Firestore. Use the following commands:
```
pip install requests
pip install google-cloud-firestore
```

Download the service account key from your Google Cloud project by navigating to "IAM & Admin" > "Service Accounts." Generate a new key and save the JSON file to your local machine. Set the `GOOGLE_APPLICATION_CREDENTIALS` environment variable to the path of this JSON file to authenticate your application:
```bash
export GOOGLE_APPLICATION_CREDENTIALS="/path/to/your/service-account-file.json"
```

Write a Python script to fetch data from TMDb using their API. Use the `requests` library to send HTTP requests. For example, to get popular movies:
```python
import requests

api_key = 'your_tmdb_api_key'
url = f'https://api.themoviedb.org/3/movie/popular?api_key={api_key}'
response = requests.get(url)
data = response.json()
movies = data['results']
```

Use the `google-cloud-firestore` library to store the fetched TMDB data into Firestore. First, initialize the Firestore client and then create documents in a Firestore collection:
```python
from google.cloud import firestore

db = firestore.Client()
collection_ref = db.collection('movies')

for movie in movies:
doc_ref = collection_ref.document(str(movie['id']))
doc_ref.set(movie)
```

This guide should allow you to manually move data from TMDb to Google Firestore without relying on third-party connectors or integrations. Adjust the scripts as necessary to fit your specific data needs and structure.