Ensure your Microsoft Dataverse environment is properly configured. Verify that you have access to the data you intend to export. You can do this by logging into your Microsoft Power Platform account, navigating to the Dataverse section, and confirming the necessary permissions and data availability.

Use the built-in export feature in Dataverse to extract your data. Navigate to the table you want to export, click on 'Export Data', and choose the format suitable for your needs, such as CSV or Excel. Save the exported file securely on your local machine.

Convert the exported data into a format compatible with Google Firestore. If you exported your data as a CSV, you might need to write a script in Python, Node.js, or another language to transform this CSV data into JSON format, as Firestore requires data in JSON.

If you haven’t already, create a Google Cloud Platform account. Go to the Google Cloud Console, create a new project, and enable Firebase services to access the Firestore database. Ensure you set up billing as required by GCP to use Firestore.

Install the Firebase CLI and initialize Firestore in your project. Run `firebase init` in your project directory, select Firestore when prompted, and configure your Firestore rules and settings. This sets up the Firebase environment locally.

Create a script to upload your prepared JSON data to Firestore. You can use the Firebase Admin SDK in a language of your choice. The script should authenticate using your Firebase service account credentials and use Firestore's API to write data into the database. Here’s a simple outline in Node.js:
```javascript
const admin = require('firebase-admin');
const serviceAccount = require('path/to/your/serviceAccountKey.json');

admin.initializeApp({
credential: admin.credential.cert(serviceAccount)
});

const db = admin.firestore();

const data = require('path/to/your/data.json');

data.forEach(async (item) => {
await db.collection('your-collection-name').doc(item.id).set(item);
});
```
Replace `'path/to/your/serviceAccountKey.json'`, `'path/to/your/data.json'`, and `'your-collection-name'` with actual values.

After uploading the data, verify its integrity by checking your Firestore database through the Google Cloud Console. Ensure that all records are accurately transferred and that there are no discrepancies. You can write additional scripts to compare record counts or specific fields between your original data and Firestore data to confirm successful migration.

By following these steps, you should be able to move your data from Microsoft Dataverse to Google Firestore without relying on any third-party connectors.