What is the expiration of the i-94? I'm assuming it's a month or less. The SSA office will not issue a ssn to you if you are that close to the expiration on the I-94 and you will have to wait until you receive your EAD (assuming you applied for this) otherwise you will have to wait until you get your greencard.
After you receive your EAD/AP combo card, take it, and a completed SS-5 application, to a SSA office. The SSN card you will receive will have the "Valid for work only with DHS Authorization" statement on it. The I-765/I-131 EAD/AP Combo card (or later Green Card (GC)) is the requisite DHS authorization document. After you receive your 2-yr conditional Green Card, you can take it, and a another completed SS-5 application to the SSA office and apply to receive another SSN card without the "Valid work..." statement on it.
