The card is irrelevant. It may take a few weeks to mail it and it may get misdelivered or lost. But, as soon as you are approved, you will have a KTN which you may enter into your air carrier profiles or PNR data. The card itself has some occasional uses, but none of them relate to your status in GE.
Give it a few weeks and send a note to CBP on the contact form if it does not arrive.