Before starting the data transfer, ensure you have the necessary tools and environment set up. Install CockroachDB and the Google Cloud SDK on your machine. Ensure you have access to both CockroachDB and a Google Cloud project with Firestore enabled.

Use SQL queries to extract the data you wish to transfer from CockroachDB. You can use a command-line tool like `cockroach sql` to connect and run queries. Export the data to a CSV or JSON file for easier manipulation later. For example:
```bash
cockroach sql --execute="SELECT * FROM your_table;" --insecure --host=your_host > data.json
```

Transform the extracted data into a format compatible with Firestore. Firestore uses a JSON-like structure, so if your data isn’t already in JSON, you’ll need to convert it. Ensure the JSON structure reflects Firestore’s document model, with key-value pairs nested appropriately.

Authenticate your machine with Google Cloud to allow API calls to Firestore. Use the `gcloud` command-line tool to set up authentication:
```bash
gcloud auth application-default login
```
Ensure the account used has permissions to write to Firestore.

Write a script in a language like Python, Node.js, or Go to read the transformed data and upload it to Firestore. Use Google’s client libraries to facilitate this. For instance, in Python:
```python
from google.cloud import firestore

db = firestore.Client()
with open('data.json', 'r') as file:
data = json.load(file)

for item in data:
doc_ref = db.collection('your_collection').document(item['id'])
doc_ref.set(item)
```

Run your script to transfer the data from your local environment to Google Firestore. Monitor the execution for any errors or issues. If the dataset is large, consider batching the uploads to avoid rate limits or timeouts.

Once the data transfer is complete, verify the integrity and completeness of the data in Firestore. Use the Firestore console or queries to check that the documents match the source data from CockroachDB. You might also want to run some automated checks to compare counts or specific fields between the two databases.

By following these steps, you can manually transfer data from CockroachDB to Google Firestore without relying on third-party connectors or integrations.