Quick question. Which version of MySQL were you running? 5.6 is single thread on the slave and falls behind more easily. 5.7 gives you multiple threads and does a better job of keeping up.
Whichever the highest version offered in the second generation Google Cloud SQL offering as of November/December 2016. If 5.7 was available, I would have chosen that. I don't specifically recall though.
Disclosure: I work on Google Cloud and Cloud SQL