Can I petition my son if my green card hasn't arrived yet?

While the USCIS may be slow in completing many of its responsibilities, it is reasonably swift in issuing "Green Cards" after an Adjustment of Status application formally has been approved. Usually the Card is issued within about 10 days, and it is official proof of one's new status. When an approved applicant has an urgent need for proof that he/she is a Permanent Resident, an INFOPASS appointment may be scheduled with the USCIS to obtain a temporary stamp in the passport as proof of new status. The actual Card or the stamp would be necessary for a new family-based application - a Social Security Card and Advance Parole (a "work permit") would be insufficient - and note that the work permit would become void and should not be used for any purpose once someone actually has become a Permanent Resident. It would be wise to engage an immigration attorney who could help you properly prepare and fully document an application for your son that could be ready to file at the very earliest moment. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

You can try filing the petition if you have proof of your permanent resident status.