Is it realistic to aim for consulting with no prior experience? (Rising Junior)

Background: Just finished my sophomore year at Columbia as a political science and history double major with a (very sightly above) 4.0 GPA.

I've recently become interested in pursuing consulting after talking with some recent graduates and alums who work in consulting. Problem is that I have absolutely no prior experience with anything relating to consulting. My long term goal always was (and still is) law school, so last summer I interned with a judge and this summer, I have a fellowship to intern at a criminal justice non-profit. I also have some general office work experience through on campus work-study jobs but again nothing consulting or business related. I also haven't taken any quantitative classes in college, and I really don't have any space in my schedule to take any in the future because of my double major and study abroad plans.

Considering that I am already a rising junior and have done nothing to prepare to break into consulting, is it realistic to aim for a consulting internship for next summer or a job in consulting after graduation? I have time to prepare for case interviews and stuff like that this summer, but I just want to know if I actually have a shot at breaking into the field before I start doing all that.

Also, any general advice on how to get into consulting and resources to use to learn more about the process would be really appreciated. I have only just begun to look into the process and I know I have a lot to learn!