Admitting candidates from a no-name college?
Every student, whether they come from a well known or an obscure university has to make his or her own case for admission. While it is easier to accept that the education from a well known place is adequate it isn't impossible to evaluate the record from someplace not yet represented in the student population. Some colleges have people who will do this as a matter of course. 

Perhaps one or more of your professors can help. Sometimes the web of academic personal reach in a given field is quite broad.

But the case is still yours to make. You should demonstrate in your materials that you not only have taken courses at your university, but that you have learned the essential things needed to advance further. The presumption that MIT, for example, turns out skilled students is, for the most part, justified, but it doesn't imply that NOT-MIT cannot also do so. 

But you need to make your case.