I very much felt the same way at the beginning of the process (and throughout the process). But you've got to remember that the worst thing that can happen is they say no. And saying no doesn't necessarily say anything about you, interviews can get derailed by any number of things none of which imply that you are unqualified. I have blanked on obvious things, i have coded horrible mistakes on whiteboards. That doesn't mean i was unqualified though.

Google never visited my university either, but i got approached for an interview (linkedIn ftw) and i accepted it because saying no, or not applying is like turning down free lottery tickets. you might not win but it doesn't hurt.