Your manager can actually be helpful, but the process is byzantine. In my case, my promo committee approved my promo. However, at L6 there was an automatic review of all promos to that level by a 2nd committee. The review committee denied my promo. My manager came in at this point and lodged an appeal on my behalf to the review committee's decision. That appeal took the promo to a 3rd committee that ultimately approved it.
I did not know any of the details of what was happening. I only learned what happened in my 1:1 with my manager when he told me the whole story. He was so happy and proud of himself that he managed to help me get promoted. The sad thing is that this was the 1:1 where I told him that I was leaving for Netflix (much better offer due to non-monetary factors).
The truly kafka-esque part of this: Since promo at Google is a huge deal, and since you if you are hired back, you retain the level at which you departed at, I really wanted to leave as a L6. So I delayed my start at Netflix until my promo went through. I resigned effective a day after the effective promo date. However, in the HR system, the resignation cancelled the promo. So I had to jump through some hoops to get the promo re-instated. I know it went through, because I had friends check go/epitaphs and I eventually got my promo jacket..