First, create a Google Cloud Platform (GCP) project if you haven’t already. Go to the GCP Console, click on the project dropdown, and select "New Project." Follow the prompts to set up your project.

Navigate to the "APIs & Services" section in the GCP Console and enable the BigQuery API. This will allow you to interact with BigQuery programmatically.

Sign up for a Polygon account if you haven’t done so. Once registered, navigate to the API keys section on the Polygon dashboard and generate an API key. This key is necessary for authenticating your requests to the Polygon Stock API.

Create a Python script or use another programming language of your choice to fetch data from the Polygon Stock API. Use the `requests` library in Python to make HTTP requests. Here is a basic outline of how your script might look:

```python
import requests

API_KEY = 'your_polygon_api_key'
url = f"https://api.polygon.io/v1/stock/ticker?apiKey={API_KEY}"
response = requests.get(url)
data = response.json()
```

Ensure you replace `your_polygon_api_key` with your actual API key.

Process the data received from the Polygon API into a format suitable for BigQuery, typically JSON or CSV. Ensure that the data structure aligns with the schema of your BigQuery table. For example, convert timestamps into a standard format and ensure all fields have consistent data types.

In the GCP Console, create a Google Cloud Storage bucket. This bucket will temporarily store your data before loading it into BigQuery. Go to the “Cloud Storage”� section, click “Create bucket,”� and follow the prompts to configure your storage bucket.

Use the BigQuery client library to load data from GCS into BigQuery. Here’s an example using Python:

```python
from google.cloud import bigquery
from google.cloud import storage

# Initialize clients
bigquery_client = bigquery.Client()
storage_client = storage.Client()

# Upload data to GCS
bucket_name = 'your_bucket_name'
bucket = storage_client.bucket(bucket_name)
blob = bucket.blob('data.json')
blob.upload_from_filename('path_to_your_local_file')

# Load data from GCS to BigQuery
table_id = 'your_project.your_dataset.your_table'
job_config = bigquery.LoadJobConfig(
source_format=bigquery.SourceFormat.NEWLINE_DELIMITED_JSON,
autodetect=True,
)

uri = f'gs://{bucket_name}/data.json'
load_job = bigquery_client.load_table_from_uri(
uri, table_id, job_config=job_config
)

load_job.result() # Waits for the job to complete.
```

Replace `'your_bucket_name'`, `'path_to_your_local_file'`, and `'your_project.your_dataset.your_table'` with your actual storage bucket name, local file path, and BigQuery table ID, respectively.

By following these steps, you can seamlessly move data from the Polygon Stock API to BigQuery using Google Cloud's native tools and services.