'Google BigQuery: Add new column to a table with constant value

I would like to know a way of adding one additional column to a BigQuery table, that will populate all the rows for this newly created column with specific constant value. I know how to create column with NULL values:

ALTER TABLE project_id.dataset.table
ADD COLUMN A STRING

But my goal is to also add the ingestion time with CURRENT_TIMESTAMP() function. Is it even possible with one command? Or maybe I need to apply subsequently some second command?



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