We’ve written a guide on how to import a MySQL database into a Cloud SQL instance while minimising downtime. The trick is to take an initial dump of the database at your leisure, and then use the MySQL binary log to do subsequent incremental migrations.
I recently used this technique to migrate a 20GB production database, with a relatively high rate of new writes, to Cloud SQL with less than 1 minute of downtime.
The initial dump and load took almost 3 hours, during which time the app was unaffected. The final incremental catch-up took just a few seconds, and then a few seconds more to reconfigure and restart the app.
This will help you get onto Cloud SQL quicker so you can start taking advantage of the automated updates and scheduled snapshots etc.