Run SQL commands to verify the migration. For example:
At the postgres prompt, enter \list to list the databases and verify that you see your source database instance.
At the postgres prompt, enter \connect SOURCE_DB_NAME, and enter the password when prompted, to connect to the database instance and see the tables associated with the instance. The name of the prompt changes from postgres to SOURCE_DB_NAME.
At the SOURCE_DB_NAME prompt, enter \dt to see the tables of this instance.
At the SOURCE_DB_NAME prompt, enter GRANT cloudsqlexternalsync to USER; because you want to give this user permission to access the data in the tables of this instance. Also, replace USER with the name of the user you used to connect to the destination database instance.
At the SOURCE_DB_NAME prompt, enter SELECT * from TABLE_NAME; to see the information that's replicated from a table in your source database instance.
Verify that you see the correct information in the table.
If everything you check is as you expect, then Database Migration Service has migrated the data correctly.