She found me.
While easier than your situation, the closed adoption process is specifically designed to prevent either of us from finding the other. With open adoptions, everyone knows everyone's identity and they agree on how much information sharing goes on as the child grows up. Closed adoptions are meant for people who don't want the birth parents to have any role at all. In the US, closed adoptions were the norm for government childcare facilities until perhaps the 1990's. Certainly, there were a lot of private adoptions that were more open.
With today's internet, finding someone doesn't seem difficult, but my birth mother had to do it "old school." The adoption agency gave her a few facts about my family (married couple with two young boys, adopted girl, living in Los Angeles) and used those facts to query preschools, hospitals, church groups by mail to see if anyone might know us. She collected enough facts to eventually bribe a worker at the state's drivers' license agency to give her the address of my brother. She then posed as a friend of mine, called my mother, and got my phone number. It took her many years and hundreds of letters and phone calls. I give her credit for her tenacity.
I am generally not a religious person, so I naturally question religious influence over decisions such as this one. However, she was a very naive woman, very alone, and I think they did both of us a good service by steering her to the home for unwed mothers. It took her 9 years to get her life together, and during those 9 years, I thrived in a stable, loving, safe home.
As you were abandoned, it will be difficult for you to find your birth parents. However, have you heard of a web site called 23 & Me? It takes your DNA and compares it to a bunch of DNA databases, and then tells you where people with close genetic matches might live. You are able to connect anonymously with that person (if they are willing). Someone on Reddit found a cousin recently. Just be careful what you wish for, because not all reunions end up happy. It can be soul crushing if it doesn't work out the way you hope.