I don't think there is a direct way to do this replicate between Bigquery and Cloud SQL.
To copy data from Big query to Cloud SQL one option I could think of is Export/Import:
- First export the data in CSV format in GCS and then import the same in cloud sql. Also because of the export limitation in BQ, for tables larger than 1 GB we need to export to multiple files into GCS bucket
- Import Operation into Cloud SQL, we can use psql copy command
Sample Copy Command which we can run from VM(VM instance to have access to GCS bucket Source and Target Post Gres):
gsutil cat gs://<bucket_name>/<csv_filename> | psql -h <CLOUDSQL_IP> -d -U -c "\copy from stdin with (format csv)"
[1] https://cloud.google.com/bigquery/docs/exporting-data
[2] https://www.postgresql.org/docs/13/sql-copy.html