So only you, the USC is getting deployed? If yes, then just get started now on I-751 (make sure it's the latest edition of the form), and have wife compile the rest of the evidence by the time the deadline to send in the form in comes. You can pre-sign the completed form. She'll include your contract in the evidence alongside the other required evidence - drivers license, bank statements, utility bills, childcare/doctor notes listing both of you as parents of the child...