No, unfortunately not. Consider yourself lucky that you got your present EAD as part of your OPT, and don't try to "muddy the waters" or otherwise create problems for yourself in attempting to contact USCIS to ask them to "advance" the EAD's validity date. USCIS advances nothing, ever. That having been said, nothing prohibits you from presenting yourself to the employer sooner, as an "observer", perhaps? Talk about this with your school's DSO and see what he or she has to suggest in that regard.
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