I have a MS from a top math program, and I languished for 2.5 years unemployed. I was fortunate enough to land a first job in frontend web development & invested countless hours learning & experimenting on and off the job. I do quite well now financially, and am satisfied with where I am at.
Since you're employed, your career is up to you. Some people luck into high powered salary tracks off the bat - for the rest of us, hard & smart work is necessary to compensate.
So the trick with an application mosh pit like that is one of two things: (1) insider connection (a friend recommends you or gives you the email of the person with hiring power, you email them directly with a coherent, company-specific cover letter + resume), and (2) informational interviews. With informational interviews, you reach out to someone with the role you're interested in and say you want to visit, get coffee, or chat over the phone to get a sense whether this field + role are a good fit for you. No, you're not necessarily applying, you're doing research to figure out if you and the position/company are a good match, for a prospective job change down the road. You're interested in specifics: nature of day-to-day work, nature of problems, best/worst things about the company/field. That really throws people. It impresses them and reverses the whole dynamic. You're not the groveling supplicant anymore, begging for job-crumbs... you're an autonomous person who knows his/her own worth and is shopping for a good fit. That's powerful stuff that commands attention and gets you interesting referrals, maybe even back to their friends at the big companies.
- Cover letter too generic. Fails to identify (1) the company, (2) what it does, (3) why you specifically are a great fit for the specific position you are applying to
- Forgot to sculpt your CV to fit the narrative of your cover letter. The CV isn't some static life scoresheet, it's a short story that changes between applications.
- Responds to questions designed to test the outer limits of your knowledge by getting anxious, inventive, and defensive, instead of taking it as an opportunity to (1) acknowledge your lack of expertise, (2) describe a creative application of related relevant experience, and (3) state your eagerness to learn the specific topic they were asking about.
- Apologized for yourself in the interview in any way. Why don't you have more internship experience? GOOD: "Well, I was interested in really focusing on my thesis at the time, but now I want to work in the private sector, and this role in particular really intrigues me. It's actually relevant to what I was doing before in that..." BAD: "Er, well, I don't know, haha, probably should have? Sorry..." Apologies are off-topic. They interrupt your narrative. Don't apologize.
- No proofreading + chance encounter with grammar nut. (But your comment was really elegantly written, so I doubt that's your problem.) Sloppy dresser + chance encounter with sartorial nut. Etc. Don't give some meanie a reason to reject you. Don't break the spell of your story.
- Didn't have any good questions at the end of the interview. Questions traditionally go at the end and in some ways it's unfair to do this to people, because by then they're usually enervated and ready to bolt... but this is the GRAND FINALE, the point where you REALLY need to drive the narrative home.
Lots of people are going to tell you to practice technical interviewing and that's important, but be sure not to neglect the NARRATIVE element of the application. Identify the company, identify you, explain why it's a perfect match. Repeat the same narrative in the CV, the resume, the interview, and the thank you note. That's how you defeat "meh".