If I am able to understand your question, you have data in GCS Bucket that you are using in Google BigQuery table/View.
Now you have created an integration and external stage using snowflake on top of the same data in GCS bucket and can see the data as well - right?
There is no direct link to load data from Google Big Query to Snowflake Table. You have either unload the data into the GCS bucket or use the same original data to load into the snowflake using the article below:
You can load the GCS Bucket data into Snowflake using the below article:
https://community.snowflake.com/s/article/Loading-Data-from-Google-Cloud-Storage-to-Snowflake