When Nia saw the Kamina statues, she knew just how much Simon loved him and how important Kamina was to him. And seeing how he could feel so much for a person, Nia thought she could believe in him.
Nia is well aware that she doesn't know everything about her friends, but she tries very hard to learn more, and she continues believing in them because from her observations, she thinks they're trustworthy. Even when the Great Gurren Brigade were suspicious of her in the beginning, she told Simon that she still got a warm feeling from them and thought they weren't bad people. And Simon was always there for her where her father was not. When she found out her father just thought of her as a doll, Simon told her she should just live as herself, accepting her as a human being. After all that, why should she doubt him? That's just how she views things.
Her personality was about “questioning everything”, what everyone else considered an absolute she tried to actually understand. “Why are you fighting?”, “Why do you love me?” or the like. Beyond that, she had core motivations and her personal reasoning on the world. Actions like when she told Simon to use her hands as cushions for piloting Lagann or lines like “Farewell, Father. I’ll look towards tomorrow” or “As a matter of fact, we’re completely different persons. But I believe that thanks to these differences we will be able to live together” among others are clearly unique and meaningful.