Relocating for a job while trying to aggressively pay loan

Title is a bit of an oxymoron. For context, I am a recent grad who took a role in NYC where they are requiring me to move to jersey city area at least (they said nyc but I don’t want to live in nyc).

I’m going to be making 100k, but I’m realizing that’s not really a lot after taxes and paying things off like my loan and rent. I’m not sure how much my rent will be yet, I haven’t moved yet.

I have 41k in loans, and want to pay it off. I am a cs major and will be a software engineer. This job honestly feels like a L. I’m not saving as much as I could if I stayed at home, I’m not paying off the loan as much as I could. I had an offer at a defense contractor, but clearance was taking so long and needed to find something before I was required to make payments on my loan (May 2025 grad). I guess I just got impatient, but I also might have fell for the fallacy that defense contractors will have me outdated. The contractor was going to pay me 82k and I would be living at home with my parents. I brought it up to my mom how I want to aggressively pay it off, but I don’t think this job will allow me to do that especially with one of my loans have 6.7% interest. All of my loans are public.

I’m not sure how long I should stay at this job. They’re giving me 5k relocation stipend, but I would have to pay it back if I leave before a year.

I feel like I kinda took a losing offer here. Should I stay for a year so I get more experience on my resume? Or try and find something closer to my house where I can live at home after spending 6 months here.

I feel like I made a bad choice.