A while ago I asked the same question to the GAP support team and their answer was that the fullVisitorId in BigQuery is a hash form of Client ID, so the Client ID from the _ga cookie isn't represented directly in BigQuery.
In other words, a single Client ID will map to a single fullVisitorId, but you can't get the client ID in BigQuery (unless you capture it as a custom dimension).
Update:
Starting on May 24, 2018, Google began exporting the Google Analytics Client ID to BigQuery. The schema addition details are:
-------------------------------------------------------------------------
| Field Name | Type | Description |
-------------------------------------------------------------------------
| clientId | STRING | Unhashed version of the Client ID for a given |
| | | user associated with any given visit/session. |
-------------------------------------------------------------------------