This depends a lot on you, your ability to apply your knowledge of statistics, computer science and mathematics to abstract problems and also your problem solving intuition and prowess. A great many jobs in the US require Masters or Ph.D.s, but there are some that do not. But add to this, your lack of a degree in a truly quantitative discipline and it might make things tough.
Though you have cited some background in statistics, being a data science requires that you have the mathematical maturity to digest research papers and text books to apply abstract concepts to the real world. This typically requires the experience that is common to a mathematics BS or a Masters or Ph.D. in a slightly less rigorous field like engineering.
I would certainly consider taking 2 years of calculus and enough linear algebra to get past matrix manipulation and really understand Fourier analysis, orthogonal vector spaces and Hilbert space.
I would advise you to seriously consider a Masters or Ph.D. program. If you don't want to do this, then try to take full advantage of your CSE minor to be a really strong programmer. You should be able to find a job in a smaller startup which will allow you to prove yourself over time. Be prepared that a lot of first time jobs may be Data Engineer positions, which require a lot of ETL and data munging.
Good luck in whatever you decide to pursue!