Which means you never did any research for a professor, or know anyone who did. At MIT there's no less than official two programs for that, the main one with very substantial financial incentives.
There's an old saying about MIT that's relevant, "Undergraduates are treated like graduate students, graduate students like junior faculty, and tenured professors like gods." It exaggerates some but it most certainly gets the first bit right, undergraduates are assumed to be capable of graduate level research. "seniors planning on graduate education becoming more active in a department, maybe getting an internship to make photo copies and coffee" is just not how it works at MIT, that's work for MIT's generally very capable office staff.
And thus if you use the research method in "'forging relationships' with faculty" perhaps after acing a course they taught, and you do well, you'll get the inherently political but not in a really bad way "in" to graduate programs when your professor tells a professor who knows your professor that you can do research, as discussed elsewhere.