Start by setting up a Google Cloud Project. Go to the Google Cloud Console, click on "Select a project," and then "New Project." Give your project a name and click "Create." This project will be used to manage access to Google Directory data through the Admin SDK.

Once your project is set up, navigate to the "API & Services" dashboard and click on "Enable APIs and Services." Search for "Admin SDK" and enable it. This API will allow you to access the Google Directory data programmatically.

In the Google Cloud Console, go to "IAM & Admin" and select "Service Accounts." Click on "Create Service Account." Provide a name and description and click "Create." Grant the service account the "Domain Wide Delegation" role, which will allow it to impersonate users in your Google Workspace domain.

After creating the service account, go to the "Keys" section. Click on "Add Key" and select "JSON." This will download a JSON file containing your service account credentials. Store this file securely on your local machine as it will be used to authenticate API requests.

Log into the Google Admin Console using an admin account. Navigate to "Security" > "Access and data control" > "API controls." Under "Domain-wide delegation," click on "Manage Domain-wide Delegation." Add a new client ID using the service account's client ID and grant it the necessary scopes for accessing directory data. For example, use the scope `https://www.googleapis.com/auth/admin.directory.user.readonly` to read user data.

Write a script in your preferred programming language (e.g., Python) to authenticate and fetch data from the Google Directory. Use libraries like `google-auth` and `google-api-python-client` to handle authentication and API calls. Use the credentials from the downloaded JSON key to authenticate and access the directory data.

```python
from google.oauth2 import service_account
from googleapiclient.discovery import build

# Path to your service account JSON key
SERVICE_ACCOUNT_FILE = '/path/to/your/service-account-file.json'
SCOPES = ['https://www.googleapis.com/auth/admin.directory.user.readonly']

credentials = service_account.Credentials.from_service_account_file(
SERVICE_ACCOUNT_FILE, scopes=SCOPES)

# Impersonate a user within your domain
delegated_credentials = credentials.with_subject('admin@yourdomain.com')

service = build('admin', 'directory_v1', credentials=delegated_credentials)

# Fetch users
results = service.users().list(customer='my_customer').execute()
users = results.get('users', [])
```

Once you have fetched the data, you can write it to a local JSON file. Use standard file handling techniques to create a JSON file and write the data.

```python
import json

# Define the file path for the JSON output
output_file = 'google_directory_data.json'

# Write the data to a JSON file
with open(output_file, 'w') as f:
json.dump(users, f, indent=4)

print(f"Data successfully written to {output_file}")
```

By following these steps, you can successfully move data from Google Directory to a local JSON file without relying on third-party connectors or integrations. Adjust the script as needed to suit your specific data access requirements.