Hello, my name is Greg.
Unfortunately this is not as easy as it used to be....
Is there anything in your, or your family, possession it might be on (old tax forms, old passport, etc) - if not, you will need to send away to the Social Security administration (has a $29 fee when you do not know the SSN) - provide as much information as possible - they get back to you rather quickly.
Unfortunately there is not a public database of ssn numbers (due to so many privacy and identity theft issues in our day and age). These used to be available through a search on the SSA site but that ended a few years ago.
CLICK HERE For the PDF form to fill out to get the information.
Sorry there is not an "immediate" answer to your question. Please be sure to rate my response positively as that is the only way I receive any credit for my help today.
Have a wonderful rest of the week and all the best as you being your college journey.
I was just wanting to reach out to see if you needed any additional followup on this question. Feel free to reach out if needed.
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Have a wonderful week.