Easier: At the best, cheap in-state college, major in math, science, or tech. Do well, and then for an Ivy, etc. college, go there as a grad student which can be even better for meeting people than being a ugrad student at an Ivy. Going as a grad student might be for free.

Maybe teach some ugrad courses -- a way to meet people, especially girls 1-3 years younger. Generally do a lot of the obvious things to meet people -- much of the reason for an Ivy is to meet people. If you want an academic career, then a top research university can be a HUGE help, i.e., may have several world class research professors any one of whom could get you a good start on an excellent research direction.

As a ugrad, to help getting into the college you want as a grad student, be sure to work hard and do well. E.g., any free time you might have, get and study the books of courses you plan to take. Then in such courses you will have a head start that can make you look MUCH smarter. For some of the profs that taught courses you did well in, get them to help you with suggestions of courses, texts, papers. You will want one or more such profs to recommend you for the grad program you want. To do well, maybe write an honors paper.