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in my case, my lawyer did the EAD application along with the I-485 on Dec 01, 2000. I got my EAD approved on 04/11/2001 due to AVM. I received my EAD card on 04/25/2001. So almost 4 and half month. But it all depends on the current situation. It will be a good idea to get your EAD card on your hand in case something happen later.
good luck!