Once you are there, I'd say the best way would be to find someone in your network who works at google, and get referred. If you don't know anyone, make contacts through various channels.
Is this you personal experience?
I know for a fact that almost no one I interviewed with bothered to look at github. Some even admitted that asking for github is just a formality and that they don't have time or resources to evaluate it objectively.
I also concur that getting a referral from an any employee that you might meet is the better than just blindly sending in your resume, though not as good as a strong referral (i.e. someone you've had direct experience working with before). You will get more attention from the HR side and the employee referring you will have a better idea of what teams will be relevant than the HR people will.