You can migrate your sites over to DigitalOcean and test them using your hosts file on your PC and make sure everything is working fine before switching the DNS to DigitalOcean. In this way you can make sure everything is working properly on DigitalOcean and you will prevent any issues when switching the DNS. If you’re not familiar with the process let me know and I can provide you with detailed instructions in order to set your hosts file.
When you switch the DNS from Google Cloud to DigitalOcean there will be some propagation and some of the visitors may still “see” the version hosted on Google’s end. DNS changes might take up to 48 hours due to DNS cache from all the ISPs, but usually happens a lot faster.
Simply switching the DNS over should be completely fine. I don’t know if you’re running an eCommerce website or a simple blog, but even if someone places an order on your site or publish any comment/post and etc you can still re-migrate only the missing content/database table/row in order to make sure everything is updated on DigitalOcean end.
Another solution is that during the DNS propagation you can simply put a holding (coming soon/under maintenance page) for an hour or two in order to prevent any issues. This is something I’ve done before in order to make sure no one will visit the version on the old host during the DNS propagation.
If you have any questions, feel free to ask.