Begin by setting up the Google Cloud SDK on your local machine. This toolkit will allow you to interact with Google Cloud services directly from your command line. Download and install the SDK from the official Google Cloud website. Once installed, authenticate your account using `gcloud auth login` and set your desired project with `gcloud config set project [PROJECT_ID]`.

In the Google Cloud Console, navigate to the Pub/Sub section and create a new topic. A topic is a named resource to which messages are sent. Use the console or the command line with `gcloud pubsub topics create [TOPIC_NAME]` to create your topic.

Use Python to read the Parquet file. Python's Pandas library, along with PyArrow, can be used to handle Parquet files. Install these libraries with `pip install pandas pyarrow`. In your Python script, use `pandas.read_parquet('yourfile.parquet')` to load the data into a DataFrame.

Convert the data from the DataFrame into JSON format, as Pub/Sub messages are typically sent as JSON strings. You can achieve this using Pandas' `to_json()` method. For example: `json_data = df.to_json(orient='records')` which will convert the DataFrame into a JSON array of records.

Use the Google Cloud Pub/Sub client library for Python to publish messages. Install it with `pip install google-cloud-pubsub`. Initialize a Publisher client and use it to send messages. Iterate over the JSON data and publish each record as a message to your topic using:
```python
from google.cloud import pubsub_v1

publisher = pubsub_v1.PublisherClient()
topic_path = publisher.topic_path('[PROJECT_ID]', '[TOPIC_NAME]')

for record in json_data:
publisher.publish(topic_path, data=record.encode('utf-8'))
```

Ensure that the account you're using has the necessary permissions to publish messages to the Pub/Sub topic. This usually involves setting up a service account with the Pub/Sub Publisher role and exporting its credentials to your environment with `GOOGLE_APPLICATION_CREDENTIALS='/path/to/your/service-account-file.json'`.

After the data is published, verify the messages are reaching the Pub/Sub topic. You can do this by creating a subscription to the topic and viewing the messages. In the Google Cloud Console, navigate to Pub/Sub, create a subscription for your topic, and use the console or command line to pull messages to ensure data integrity and successful transmission.

By following these steps, you can efficiently move data from a Parquet file to Google Pub/Sub without relying on third-party connectors.