Data Science is possible, but generally seems hard to break in without prior programming experience or a masters or higher - I had problems getting in as a 4 year PhD dropout from a prestigious math program, and ended up teaching myself programming & have carved out a nice career as a software engineer. My math & physics background has proven to be a bonus in my favor when interviewing, and I generally am favorable to people with a math background I encounter in industry/interviewing candidates since I have found it fairly uncommon.
I would go to on campus career events if possible, and talk with company recruiters about interviewing & general tips. There are potential other options depending on how open you are to them - the options are a lot more open IMO than with most degrees. One thing that might help is to go to Indeed, LinkedIn, etc., and just search for jobs in a particular area - if a particular profession sounds like something that might be feasible/palatable for a career or first step, jot down the title, and continue. This doesn't mean you're committing to anything in particular, but it will help you understand what you are looking for better and better prepare for any future interview sessions where they ask you what got you interested in .