I work for a large state university and run linux on my office machine, despite the fact the IT office dept doesn’t officially support it. I told our IT guy once what I’m doing and his response was, “cool.” Of course I’m totally on my own if anything goes wrong. It helps that I’m a prof and most of my on-campus work doesn’t involve much time on a computer, aside from basic web and documents stuff. tldr, in my case I’m able to just do it without asking anyone’s permission, and it’s worked out great for several years now, but a lot of jobs aren’t like that obviously.
You say this machine is headless. Is it at a remote location? If not, is it feasible to connect it to a monitor an keyboard for a few minutes? If so then you could logout, switch DE, and then log back in. That would hopefully set the DE you prefer as user default.
If that’s not possible, then some of the solutions discussed here might be applicable.