Have yall ever been able to find your birth parents? If so how did you do it?

So I was adopted at birth pretty much, I was with my birth mom the first 2 days and then transferred to my adoptive family. Over the years I’ve found out small details, and more recently found my birth report with some of my birth mother’s info on it, minus her last name. No info whatsoever on my birthfathef (I was most likely the result of an unplanned pregnancy). My life with my adoptive family has been wonderful and I’ve loved every moment!

I want to find her just to know who she is and maybe meet her someday. How could I go about finding her when I don’t even have her last name, I have her first name and birthday and that’s the most crucial details I really have.