Based on how you phrased the question, I'm not sure trying to directly leverage a service like Google Cloud Platform or Amazon Web Services is necessarily the right choice. I would characterize "let's use Google Cloud Platform to run a phpBB instance" the same way I would characterize "let's rent a blank virtual server from a hosting company to run a phpBB instance."
That "blank virtual server" definitely can
be used to do what you want. But now "all the problems of getting the platform setup to run the database engine you need, the web server platform you need, the php platform you need, the administration tools you need, and the responsibility for keeping those services running in the future" are now your problem
You can get turn-key server appliance images
from sources like Bitnami.com
, which make "how do I get this GCP or AWS server into a state ready to run phpBB" much easier. So you're essentially buying "an empty virtual server or virtual application shell" from GCP or AWS, an then loading that empty shell with a pre-cooked appliance image from Bitnami.
How to set this up, how suitable or how well it works, how easy it is to manage or keep updated in the future, etc., are now all conversations between you and Bitnami documentation; not between you and GCP or AWS. Because Bitnami is now effectively supplying your "platform" on which your web application is running; and Bitnami in turn had created that platform using industry standard free and open-source services and refer to to the associated documentation. GCP and AWS effectively just supplied "the physical server", and their interest ends at micro-billing for the CPU time and I/O usage generated by "whatever the hell you're doing on our server."
Unless you're really positive that there is some reason you need to host this on GCP yourself
, the answer for "I need to move to a better host" is more likely that you need to start paying for a higher service tier which has more CPUs, more I/O allowance, etc., with the web hosting company you're already on. Or change hosting companies if you need to, and start paying for that same higher service tier there.
As an individual user and customer, you can
go directly to GCP or AWS to host your web application like phpBB. But you're agreeing to a higher level of "personally getting your hands dirty" in the routine maintenance, issues, and security needed to create and maintain such a platform suitable for the application. Things that your hosting company currently does behind the scenes for you and all of their customers, "without you having to lift a finger."
Whichever way you decide to do it, once you do have a web application host that is suitable for running phpBB, knowledgebase articles like "Knowledge Base - Transferring Your Board to a New Host or Domain
" talk about the steps that can be necessary in moving an existing board to a new host.