Starting October 2, 2017 an information-sharing partnership between U.S. Citizenship and Immigration Services (USCIS) and the Social Security Administration (SSA) allows individuals in certain immigration categories or classifications to apply for work authorization and a social security number at the same time on Form I-765, Application for Employment Authorization.
A USCIS News Release stated,
"Previously, applicants needed to submit a Form I-765 to USCIS for an EAD, and then submit additional paperwork in-person at their local Social Security office to obtain an SSN.
The revised USCIS [I-765] form includes additional questions that allow applicants to apply for an SSN or replacement card without visiting a Social Security office. Starting today, USCIS will transmit the additional data collected on the form to the SSA for processing."
A Social Security Administration FAQ says, "For Form I-765, we will issue your card as soon as the U.S. Citizenship and Immigration Services (USCIS) approves your employment authorization. Generally, you will get your card within 10-14 business days from the date your application is processed."