http://www.ssa.gov/ssnumber/

Follow these steps. They are very straight forward. This is the easiest part of DACA. While DACA and the EAD took several months, it should take no more than 2 weeks for your Social to arrive in the mail. It says so on the receipt letter they give you.

Also, If you can't find your birth certificate, just a passport is fine. Go into an office in person, but expect to be there at least an hour. Check your local times. The first time I went in I went at 3:30pm, I assumed the office closed at 5. Apparently they have some new policy that requirs them to close at 3pm, at least in my area.