Begin by ensuring you have PostgreSQL and the Google Cloud SDK installed on your local machine. You will also need to set up a Google Cloud project and enable the Firestore API. Make sure that you have configured your Google Cloud credentials properly using `gcloud auth login` and that you have access to the Firestore database within your project.

Using SQL commands, export the data you need from PostgreSQL. You can use the `COPY` command to export data to a CSV file. For example, run the command:
```sql
COPY (SELECT FROM your_table_name) TO '/path/to/your_file.csv' WITH CSV HEADER;
```
This will create a CSV file of your desired data.

Convert the CSV file into JSON format, which is the required format for Firestore. You can write a script in Python to achieve this. Use the `csv` module to read the CSV and the `json` module to write the JSON file. Here's a simple script snippet:
```python
import csv
import json

csv_file_path = '/path/to/your_file.csv'
json_file_path = '/path/to/your_file.json'

data = []
with open(csv_file_path, newline='') as csv_file:
csv_reader = csv.DictReader(csv_file)
for row in csv_reader:
data.append(row)

with open(json_file_path, 'w') as json_file:
json.dump(data, json_file, indent=4)
```

Install the Google Cloud Firestore client library for Python. This library will allow you to interact with Firestore programmatically. You can install it using pip:
```bash
pip install google-cloud-firestore
```

In your Python script, initialize the Firestore client. This involves importing the library and setting up the connection to your Firestore database:
```python
from google.cloud import firestore

# Initialize Firestore client
db = firestore.Client()
```

Use the Firestore client to write the JSON data to Firestore. You will iterate over the JSON data and add each record to a collection in Firestore:
```python
import json

# Load JSON data
with open('/path/to/your_file.json') as json_file:
data = json.load(json_file)

# Reference a Firestore collection
collection_ref = db.collection('your_collection_name')

# Add data to Firestore
for record in data:
# Use a unique identifier for each document
doc_ref = collection_ref.document(record['unique_id'])
doc_ref.set(record)
```

After importing the data, verify that it has been correctly transferred to Firestore. You can do this by checking the Firestore console in Google Cloud Platform to see if all the records appear as expected. Additionally, you can write a small script to query Firestore and print out the records to ensure everything is in place:
```python
docs = db.collection('your_collection_name').stream()

for doc in docs:
print(f'{doc.id} => {doc.to_dict()}')
```

By following these steps, you can successfully transfer data from PostgreSQL to Google Firestore without using any third-party connectors or integrations.