What do I need to do now to get a Bulge Bracket Internship?

So I'm currently in my freshman summer at a non-target school studying finance. Although it is a top 35 Business school, I will not pretend that it is remotely near Wharton status. I will be a sophomore next year and will dive further into the coursework. Currently this summer, I am working as an intern analyst at a mid-market M&A firm in my home city. In addition to my work to supplement my knowledge, I am also taking WallStreetPrep's financial modeling course. I know that I couldn't intern at a bulge bracket this summer, but I will apply for next. I also have connections through my church and friends of my father who are working at 3 different BB's and I told them I am very interested in working for them and that I will apply. I'm trying to expand my network and get my name in people's heads for the future. I will not, however, try to support my entire Job Search process on these leads/connections. I know that they have no obligation to give me any more consideration that another candidate. Because I don't go to a target school, I'm working to do anything in my power to counteract the associated disadvantages. In addition, which I would imagine is a standard expectation, I did well in school. I got a 3.88 my first semester and a 4.0 my second semester, averaging to a 3.94 GPA my freshman year. I plan next year to join the student investment club and the finance club. One interesting thing though is that Goldman Sachs (along with 2 other BB's) has a large (and I mean LARGE) Western U.S. Headquarters out to my city where my school is. They recruit out of my school and a neighboring school due to close proximity and a good intern track record. Is it feasible to get a B.B. internship next summer (sophomore), or the summer after that (junior) ? Or am Is it just unrealistic for any summer? What else should I be doing to try to give my self any advantage over the target school recruits? Thanks!