Enable the BigQuery export feature within Cloud Monitoring, which will export the monitoring data directly into BigQuery tables.

Use the Cloud Monitoring API to fetch the metric data and then use the BigQuery Streaming API to insert the data into BigQuery tables in real-time.

Create a Pub/Sub topic to export monitoring data, use Dataflow to process the data, and then use BigQuery sink to store the data in BigQuery.

Export the monitoring data to a Cloud Storage bucket, then set up a Data Transfer service to move the data to BigQuery.