Serious Help! Marrying a female US citizen pregnant from another man.

[immiman]

I met this girl a while back and we have really fallen deep in love. When i met her, she wasn't aware she was pregnant. We had not even started dating at that time. However, she later found out and told me she was pregnant just about a month before we started dating. It was hard for me to accept the situation but i still loved her so much and she loves me back. She has never been married, and the father of the unborn baby is her ex boyfriend. We've dated a number of months even with the pregnancy so I proposed to marry her a few days ago and she agreed. I have accepted to look after the child like its my own child. We plan on getting married and she wants me to establish my permanent residence because i am in the USA on a visa. I have been told marrying a woman with a baby that ain't yours raises a lot of suspicion and scrutiny. How do i proof my marriage is bonafide when my name is not listed on the birth certificate as the father of the child?
I really need help. Any ideas?