Google not only hires from IIT's  but also there are many other engineering colleges they go for recruitment.

It does hire from private institutions like  BITS Pilani, Goa, IIIT Hyderabad and others.

There are many candidates in Google or such companies which are chosen based on their talent and knowledge and not because they are from a good ranked college.
So knowledge is the first thing you should focus upon. Improve your skills and be a master in it.

Good luck.

Google looks for individuals having extraordinary practicality and potential. Though, Google goes to colleges like all the prominent IITs, NITs, BITS PILANI, but there are certain other colleges in which Google MAY GO such as -

College of Engineering,Pune.
Thapar University, Patiala.
Delhi Technological University, Delhi.
Netaji Subhash Institute of Technology, Delhi.
PEC University of Technology, Chandigarh.
Manipal University etc.


Hope this helps!!!!