To answer the Q as I think it was intended, though, I would not have looked for birth parents, as I figure there was probably an excellent reason I was given up. As a young woman, I knew a number of young women who had had to give babies up, most for seriously traumatizing reasons. Often the children were the products of rape, or punishing shame to the families (this was the 60s) and would only have been reminders of an awful time. One friend was actively pursued and found by a child she had given up, a child who resembled closely his biological father, who had stalked, raped, beaten, and left for dead my friend when she was 14.
That stuck with me, and I would rather the birth parent look for me, so I would not cause them such relived trauma.