I think the initial level is mostly a function of experience. Then depending on your interview results it can go up or down. In my case I interviewed at level 5, and did well enough to be invited to come back for another round at 6.

I was super lucky to work with a gem of a recruiter at one of the FANGs who spontaneously pushed for 6 after my feedback from 5 came back positive. The other FANG was more reactive and didn't invite me back until I told them of the competing offer. So perhaps try pushing for it yourself if your recruiter is not as proactive and you feel you have a shot. Worst case they'll say no. (Or they'll say yes and you'll bomb the next round. That's not supposed to reflect negatively on your first round, although it would likely have affected me psychologically and made me less confident during the comp negotiation.)

I ended up joining a company without levels, so I'm afraid I don't have any more useful information for you than what I gleaned as a candidate.