The notice will state a specific date, but you can attempt a walk-in for an earlier date. You are not guaranteed to be accepted for a walk-in; they will decide whether to accept you at the moment when you show up, based on their discretion and how busy they are that day.
PD: Jan 2003 (EB3 rest of world)
I-485 Approved: July 2007
I am a layman, not a lawyer. What I write here is not official or professional legal advice. In addition, my answers on this forum are specific to the scenarios discussed in each thread and should not be generalized to other situations.