My birthday was in January, meaning my first month of SS eligibility was February and the earliest I could get the first check was March.
I applied on-line for social security on 12/6/20. On 2/8/21, they called me and asked me to send my passport to prove my citizenship, which I did that day. They returned it on 2/16/21. I received my first deposit on 3/11/21, which was the first time I knew that my application had been approved. The actual approval letter that I received in the mail is dated 3/14/21, and it never showed as approved on the computer before the money arrived. In fact, it never even showed that anyone was reviewing it, only that it had been received (i.e. - step 1 in the bar graph.)
Hope that helps.