Will accepting a systems engineer job make it harder to get a SWE one?

I'm a new grad (this spring) from a state school majoring in CS. I love software development, and although I only started in college, it's what I want to do in my career. However before then I wanted to be a 'sysadmin' and did a lot of Linux/DB/cloud stuff (starting with game servers and forums) so I have a good amount of experience in I guess what would be called "systems engineering." Hence why I was given a good offer at a proprietary trading firm doing just that. But I'm worried that I won't feel fulfilled or I'll have my professional growth stunted by accepting the position, and that recruiters/peers will see me as 'just' a systems engineer; even when I have a CS degree and will likely be writing code (just more along the lines of automation/scripts/some APIs) every day. On the other hand this is the best offer I've had yet (including over SWE roles) and I don't want to let it go.

Am I just overthinking this first professional role or are my fears that I'll be pigeonholed later justified?