What is this community's opinion on the best way to start out for someone who wants to be able to support their customers better running products in cloud environments?
Take the basic training online free.
Try to deploy your app. See what problems you have. Do some research.
You might be able to find paid training or a consultant to speed up your understanding of the cloud environment into which your customers are deploying, but I'd wait until you have some base level of understanding first.
Deploying the app is not complicated - just a bunch of cloud instances and object storage.
What is complicated is interlinking regions/zones, understanding current other offerings (things like lambda, serverless offerings, strategies to simplify/reduce egress, etc)
I wouldn't focus on other offerings (lambdas etc) until you are solid on fundamentals (the regions/zones and networking stuff) that allow you to deploy the current product.
I'm most familiar with AWS (used to teach certifications for them) and think you'd benefit from studying for the AWS solution arch - associate exam. It focuses on core cloud concepts and AWS. Given the customer distribution, that's where I'd start.
I have a relatively string on-prem background (decades)
Most of my customers are moving off-prem to the cloud (or going for a hybridized approach)
That trend is not going away any time soon - which is part of why I am looking for a [somewhat] simplified approach to tackling major aspects of each of the providers
(I am already pretty adept at a couple small cloud providers from personal projects and a previous employer - it's getting up to speed with offerings past VPS instances and object storage I need now)