Nevada accepts the EAD as Proof of Identity. I went today to take the Drivers Permit. (I do not have a social yet, I will get apply for one on Monday).
You can get: ID and Drivers Permit with just the EAD and something that proves your residence (Address).
When the Drivers Permit arrives in the mail (actual card), you can schedule an appointment online for a Drivers Test. By the time you are ready to take the Drivers Test, you must have the Social Security Card.
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Original:
*Delivered: 08/15/2012.
*Biometrics : 9/20/12.
*Approval Date: 10/17/12. *
EAD Received: 10/20/12. *
Social: 10/26/12.
*Drivers License: 10/29/12.
3rd Renewal:
*Shipped: 01/15/18.
*Delivered: 1/17/18.
*Acceptance: 01/19/18.
*Biometrics: 1/20/18.
*Appointment: 02/08/18.
*Expiration: 09/18.