IMO if you're working on any non-trivial backend project, then you're already a "distributed systems engineer". Distributed systems problems are everywhere in the software world if you need to manage state and consistency across more than a single machine.

If you're asking how to work on interesting distributed systems, then I'd recommend trying to work at a tech company that is either large in and of itself (i.e. FAANG), or one that makes it's money solving distributed systems problems for others (i.e. Hashicorp, Snowflake, ...).

Either way, you can get a lot of value reading famous distributed systems papers, and building your own software projects that replicate the building blocks of these systems. For example: DNS, Gossip Failure Detector, Consensus (e.g. Raft), SQL Database, etc...