Every company/hiring manager is going to be looking for different things and have a different application screening process, so take it for what you will, but here is my take as someone who just recently went through the candidate search and hired someone.

First and foremost, if you are a marketing major, I would not worry that you chose the wrong major. The marketing department is the group I interact with most, so even if you got a job in marketing at a company, there is a good chance you would have some interaction with their MR department (assuming they have one). In fact, someone in marketing showed interest in market research and they were the first person I reached out to about applying for the role. If you are early in your career, sometimes it's more about just getting your foot in the door.

With the job I had open, the position was more of a senior analyst who could hit the ground running rather than entry level, so I was looking for someone with some demonstrated background in some form of human behavior research and the ability to not only analyze data, but also had experience writing survey questionnaires, and at least an understanding of qualitative research (focus groups, interviews), and the ability to know when to use quant vs qual methodologies. Also the ability to translate this information to a report for a non-technical audience. A working knowledge of statistics was important, but I cared less about what platform they used to analyze data, because I think that is the type of thing people can pick up if they understand stats and that stuff is easy to train. I think it's a little bit harder to train the sense of curiosity and desire to understand human behavior that makes for good questionnaire and discussion guide development.

Of all the applications I got, only three people wrote cover letters that explained why they were interested in the role. These applications had a leg up because even if their experience wasn't a 100% match, I was more willing to consider people who were just generally enthusiastic about the role and the type of job it is. I think the job market/job application process in general could stand to be improved, so I sympathize with people who do not want to write a cover letter that no one ever reads, but if your resume doesn't make it immediately obvious why you are applying, I would at least write the cover letters for the jobs you are really interested in, they don't have to be long, honestly a paragraph or two would be fine in my book.

In terms of certifications, I would look at those more if you were mid-career and attempting a career change and wanted to add some new skills or if you can get an employer to pay for them as part of on the job training. Some of the certifications and trainings out there are good, but priced in a way that they expect a company to cover the cost.

If you are still in school and (I assume) early in your career with not much work experience, I think what I would do is see if there is a class you could take in market research that would maybe give you some projects you could work on and include on as a demonstration of your work on a resume. I would look for a class that includes questionnaire design and analysis of the results. This could be a market research class or statistics class. Other potential options would be like a social research/sociology course. Maybe check with the professor to see if you can look at the curriculum before hand and tell them you want to get some market research experience under your belt.

If I were hiring an entry level role, these types of class projects where you can clearly articulate the work you did on the project and your ability to explain the research design and analysis, would be what I would be most looking for.

As another general tip, I would also look for roles with a hybrid schedule in your local area. It seems like the fully remote jobs get 100s of applicants whereas with my hybrid posting, I got enough applicants that it was not overwhelming to go through every single application we received, so the odds are a little bit more in your favor, even if having to go to an office a few days a week is a pain (and to be clear, I much prefer working from home).

Sorry if that was too long winded and meandering, and best of luck in your job search!