I am a sound designer and I am at my first job (which is a full time job, I say that because it's not always the case in my field) currently.
I have a master's degree in audio, I have a demo reel which is a remake of big game trailers. I didn't really have a great portfolio (and I still really don't feel super proud about it tho it's way better now).
Basically I was looking for an internship at the end of my degree. And I got into a start-up who is basically an audio service and small game dev studio mostly because I also know how to code in Unity and I know Pure-Data and Max/MSP with some basics on audio synthesis. I am pretty technical as far as junior sound designers go, at least that's what I am told. They didn't take me for sound design in the first place. It was like "if there is sound design to do you'll do some". Cool thing is that they were some sound design to do after all. It was also lucky that they basically needed someone just like me just at the right time.
I didn't know anyone at this company, I just contacted them by mail with resume/cover letter.
At the end of my internship they didn't hire me straight up because they were not sure they would need me but they told me they would like to do so. And they did three months later thanks to a coworker there who liked me / though I was technical enough to be independant. I work there since almost 5 months.
During the internship I didn't actually do games, but now I do.
I also got an offer not long ago for a job in a large AAA studio but it didn't happen because I am not in the US. I talked a bit with the person and he told me that what they look the most is the demo reels and they basically don't give much care about anything else (he probably didn't even read my resume because he didn't know where I was from when he contacted me). Granted it was already an audio guy so I didn't have to go through the HR part (which is where your resume and whatnot matters).
This guy noticed me because I won an award (during the 3 months I was unemployed) at an event where his company won one too and he got to my website this way (I assume, he ddn't tell me but I see no other way).
TLDR : Knew a lot more than sound design even if some of it is not at a pro level (like coding), some luck, was nice enough to work with, worked well enough (followed what I was told to do while trying to take initiatives on my own (not much tho it's scary to do so as an intern!) and respected every deadline).