Advice for my friend?

My guy friend doesn’t know what to do. His ex had his baby in May. She got married to her new guy like a month or 2 ago. She refused to put my guy friends name on the birth certificate though. He’s been thinking about it because he can’t afford to take her to court for a custody battle, but now that he thinks about it the time line of the time he came inside of her doesn’t match up with when she told him she was pregnant. It was like a week in between when he came in her and her telling him she was pregnant. She has sent him a couple pictures of the baby and the baby doesn’t look anything like him. He wanted to be in the babies life and tried really hard for a while, but since she’s now married my friends lawyer says her husband has all the rights until there is a court ordered DNA test. So my friend feels like if she’s gonna fight him like this then he’s done trying until she comes at him with a DNA test.

Is that the right thing for him to do? He’s heartbroken that if it is his baby that he’s not getting to be it’s dad, but doesn’t want to be paying child support if it’s not his.