I'd recommend finding a junior security role at a Cloud-focused MSP to gain exposure and skills required at the larger firms.

Having the degree isn't everything but it shows you're motivated towards mastering the topic. We can teach you, you just gotta show up and want to do the job. There are plenty of non-scummy companies out there you can work for that'll be a great resume builder, you just need to invest the effort into finding out which companies didn't scrap the DEI rules and apply there ha.

Old person opinion. Honestly find someone within the multiple fields, your degree can be used within, as a mentor. People within technology/cyber security love networking. If you have to go within a corpartion don't fret, alot of people started there. Also be thinking about yourself as a brand because you want your own company, brand, influencer side hustle. Keep up to date with the Ai shifting landscape as well because human careers are shifting as companies try to find what Ai is going to become long-term VS the human work force. We can't not embrace Ai at this stage if technology advancement, we just have to weave around it.

or god forbid the government

Current situation notwithstanding, government work is generally pretty great. You don't have to work for a three-letter intelligence org to do work in cyber security. I'm at a research lab that does nature shit, but cyber security is still important and we have a whole branch dedicated to just that. All I'm saying is don't limit yourself.