Full Answer
The options fall into three patterns. The first is GA4's free BigQuery export: easy to switch on, but you inherit Google's event_params nested schema, the standard free export caps around a million events a day, and the data is GA4's modelled view rather than your raw store truth. The second is scheduled ETL through tools like Fivetran, Coupler.io, or Windsor.ai, which copy WooCommerce order and customer tables into BigQuery on an interval. That's fine for periodic reporting but it moves records, not behavioural events, and it isn't real time.
The third pattern is event streaming, where each WooCommerce action is captured as it happens and written to BigQuery directly. You can build this yourself with webhooks and a small ingestion service, accepting the engineering and dead-letter-queue maintenance that comes with it, or use a managed pipeline such as Transmute Engine that hooks WooCommerce server-side and streams events into your warehouse from about $89/month.
The real decision isn't the tool, it's the shape of data you want. If you need Google's analytics view, GA4 export is fine. If you need order tables refreshed nightly, ETL works. If you need raw, real-time events in a schema you control, so you can ask questions GA4 never anticipated, you want streaming.