This is an interesting problem. I think a massive part of this is how much customers are paying. If it's enough, certain parts that may be hard to automate can be done manually.
IaaC and good software packaging will help take care of your infra, but working with 3rd party managed services that may live outside of your cloud provider will vary. If the customers are paying a lot, it becomes worth the time to manually do those steps (after verifying that they can't be automated).
Let's pretend you can automate with IaaC and docker images (although any deployment style works). You can wrap that entire process into a script that will initialize and all perform tests against the infra/service.
I'm not too familiar with it outside of exam prep, but AWS (and probably the other big guys) offer the idea of an organization, which consists of multiple accounts. Makes for easier tracking, with strong isolation. Could be a route to go.
There's a lot of variables here, and as others have said, it's a tricky path. I also think it's an interesting problem and I hope you have fun solving it.