Pick the cloud that you want to support or that more of your customers want you to support.
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.
Right now, my customers are split about 50:30:20 AWS:GPC:Azure
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)
Yeah, I'd start with AWS then. Once you understand that you'll be able to map concepts to different providers.
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.
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.