Actually AWS won't help you here. I have literally been on a 2 day training course or aurora with AWS and the explanation of how to scale was actually just the same as any traditional non-cloud explanation. Correct usage of indexes, partitioning data, optimising queries (especially any non trivial query output by an ORM) and read replicas.
In terms of explosive growth if you're talking about something like google or tiktok again slapping it all in AWS will not automatically just work. There is a lot of engineering that you'll need to get to their level.
I also think you haven't really looked at the SO link I sent through with thoughtful engineering they have huge user base with a tiny footprint.
> DigitalOcean or anyone of a number good providers of good old VPSes / Cloud-lite
Not sure why you are dunking on DO here they are a fully fledged cloud provider with much the same stuff you would need. You can also run up a huge bill on DO as well.