Minimalist infrastructure is the practice of building only what you need with the fewest number of resources. This is a philosophy, not a religion, you shouldn't build bad infrastructure to achieve a minimalist design. A minimalist design should lead to good infrastructure by reducing the amount of resources under management and the complexity of the design.
When designing your system, avoid storing additional state. Often the data you want to store is already available in the system. Using the system as the source of truth can avoid the difficult business of ensuring data consistency.
As an example, let's say you want to be able to rollback a Fargate deploy if the new task definition results in a service that won't become healthy. One option would be store the working task definition in something like DynamoDB (or git or any number of bad choices). However, your ECS service already has this information: the previous, healthy service is still running. Instead of managing a