I started as a swe at a startup and then just made my job fixing our AWS and deployments going from hand deploys on EC2 to docker containers on some of the first versions of rancher.
After that I was hired at a FANG company and worked on automating data centers and service deployments as well as a ton of other stuff. Now I pretty much just go setup infra teams for people I used to work with who are at various small to medium startups.
So I don’t have a great answer for you but I would say staying away from anything where all they can tell you is “k8s” “terraform” and stuff that boils down to writing yaml or some config language all day. Additionally if you can’t get a good idea of where the company is today in the interview and where they would like to go it’s going to be sys admin stuff. In all my interviews i lay out where we currently are and all the issues that causes and go over where we want to be in a year from now and what things need to be done to get there. At the end you should feel like you fit into some part of that.
It is amazing how many hiring managers can’t give you a coherent picture of that. If all they can say is we need k8s, docker, infra as code and other buzz words without a plan the team is setup to fail.
The other way is just apply for platform eng or sre jobs at FANG and friends which will almost never be sys admin stuff although it can happen sometimes if they are listed for a team that works on the corporate side of the business.