Well, if she is legit, good luck to her... stranger things have happened in life and maybe she will find the guy.
My friend had a one night stand when she was 20. It was a drunken thing, she was at a party while visiting a mutual friend of ours at her college. This was COMPLETELY of of character for my her, it was her one and only one night stand ever. (NOT that I judge... to each their own...) She said that things just got out of hand because she had so much to drink, but it was completley a mutual choice between the two of them to have sex. A month later she found out she was pregnant. She contacted the guy (which took some doing.... she knew his first name and that he had a really weird last name, but our mutual friend remembered who he was). He was shocked and wanted NO PART of a baby. He was apologetic and offered to pay for an abortion. She considered that route, even made the appt. but couldn't go through with it. She considered adoption, but her father (who was adopted himself) convinced her not to do that, and offered to help her financially for as long as it took. She told the guy she was having and keeping the baby, and it was up to him as to how involved he would be. He chose to not be involved, at all. She chose to not name him on the birth certificate and never asked for any support (luckily she graduated college while pregnant and got a great job, and was able to live with her parents till her son was 3 to save money to put down on a house). Her son is turning 16 this spring he and is a happy, healthy, well adjusted teenager (wellllll, as happy and well adjusted as any teen can be). He was told as he grew up that his father wasn't ready to be a father and knew that his mother would do a good job raising him. As he got older, my friend elaborated. He now knows everything and he has no desire to seek out his father. My friend's parents still live at the same house, and have the same phone number so if this guy ever really wanted to seek his son out, he could have. All and all, it worked out for her and her son. Her attitude is that the guy she had the one night stand with is the only person who could have given her the son she has, and he was meant to be here. She doesn't regret having or keeping him at all.
Hopefully this girl is ok with raising this boy on her own, it sounds like she is trying to find him to just let him know he has a child.