EAD and social security question?

Ok, so i just got my EAD (employment authorization card) and im eager to start working. My main question is can i go ahead and apply for a SS#? I am an Immigrant, not on any kind of visa from my country. If i do go ahead and apply in person, what Documents do i need to take to prove who i am? Will my EAD and Consular card be sufficient i.d?