I don't think I would recommend multi-cloud right out of the gate unless you already have a lot of experience in the space or there is a strong demand from your customers. There's a tremendous amount of overhead with security/compliance, incident management, billing, tooling, entitlements, etc. There are a number of external factors that drove our decision to do it, resiliency is just one of them. But we are a pretty big shop, spending ~$10M/mo on cloud infra and have ~100 people in the platform management department.
I would recommend focusing on multi-region within a single CSP instead (both for workloads AND your tooling), which covers the vast majority of incidents and lays some of the architectural foundation for multi-cloud down the road. Develop failover plans for each service in your architecture (eg. planned/tested runbooks to migrate to Traffic Manager in the event AFD goes down)
Also choose your provider wisely. We experience 3-5x the number of service-impacting incidents on Azure that we do on AWS. I'm sure others have different experiences, but I would never personally start a company on Azure. AWS has its own issues, of course, but reliability has not been a major one (relatively speaking) over the past 10 years. Last week's incident with DynamoDB in us-east-1 had zero impact on our AWS workloads in other regions.
