If you want to move all your data to snowflake from bigquery, so I have few assumption
1. You have all your data in gcs itself.
2. You can connect the snowflake cluster from gcp.
Now your problem shrinks down to moving your data from gcs bucket to snowflake directly.
SO now you can run copy command like
COPY INTO [<namespace>.]<table_name>
FROM { internalStage | externalStage | externalLocation }
[ FILES = ( '<file_name>' [ , '<file_name>' ] [ , ... ] ) ]
[ PATTERN = '<regex_pattern>' ]
[ FILE_FORMAT = ( { FORMAT_NAME = '[<namespace>.]<file_format_name>' |
TYPE = { CSV | JSON | AVRO | ORC | PARQUET | XML } [ formatTypeOptions ] } ) ]
[ copyOptions ]
[ VALIDATION_MODE = RETURN_<n>_ROWS | RETURN_ERRORS | RETURN_ALL_ERRORS ]
where external location is
externalLocation ::=
'gcs://<bucket>[/<path>]'
[ STORAGE_INTEGRATION = <integration_name> ]
[ ENCRYPTION = ( [ TYPE = 'GCS_SSE_KMS' ] [ KMS_KEY_ID = '<string>' ] | [ TYPE = NONE ] ) ]
The documentation for the same can be found here and here