Correct me if I'm wrong, but I believe you can submit your AMCAS without an MCAT score.
Your AMCAS gets verified (this is the bottleneck step that can take a long time).
Schools won't look at your AMCAS yet, because there's no MCAT score.
Whenever your MCAT score is released, it gets added to your AMCAS.
At this point, schools will look at your AMCAS.