No wait, I need a design pattern for how to manage accounts of a SaaS service?
I'm probably not the target audience here but I strongly get the impression that these patterns would not be necessary if AWS would get their shit together in terms of AWS Console UX design.
As far as multiple accounts are concerned, this is a tradeoff you make for isolation and security. Knowing that fat fingering a staging change can not possibly impact production because the credential used in that case is literally for a different account is very comforting when you're running devops in an environment managed by multiple people.
While a lot of the stuff Amazon gives you may seem complicated, or overkill, if it's something you need it tends to be quite a bit simpler than the off-the-shelf alternative (see: VPC versus private networking).
I think the reason it might seem hard is because you probably don't have operational experience. You need to have that knowledge if you have your own data center.
Sure, this all could be abstracted, and it kind of is if you use things like Beanstalk, but AWS provides great flexibility which can make difference how your application performs in the end and how easy it is to maintain it.
Arguably Google Cloud is pretty well done, especially if you're already using their G-Suite service. What would make AWS easier for you and why did it take 3 hours to create accounts for your team?
You don't need to have some zany serverless infrastructure. The overhead in setting it up isn't worth the trouble.
Abstraction is no replacement for knowledge.