Daniel decides to walk to his barber, since he's letting the universe dictate his actions today. He wonders if God is on the street, but as soon as he exits the station into Times Square, he reasons that God would never hang out there. Daniel keeps an eye out for a sign as he walks and tries to open the doors to a church. It's locked. He sits down on the steps and watches as passersby across the street make their way around a black girl (Natasha) swaying on the sidewalk. She has big pink headphones on and looks entirely lost in her music.
At this point, it's somewhat unclear if Daniel actually believes in signs and religion, or if he's just looking for excuses to not think about his interview. When Daniel finds the church locked, it's a symbolic way to turn him away from a divine connection and towards a human one in the form of Natasha. In addition, notice how Natasha uses her headphones—they shut her off from the world.
Natasha opens her eyes. She looks embarrassed and hurries on her way. Daniel wonders what she's listening to, and thinks that only poetry makes him feel like she seemed to. He thinks he'd give anything to be passionate about being a doctor, but he feels ambivalent. As Natasha walks away, Daniel sees that "DEUS EX MACHINA" is printed on her jacket. When she walks into a store called Second Coming Records, he decides it's a sign and follows her.
Keep in mind that Daniel's first interpretation of Natasha is that she's possibly just as passionate about music as he is about poetry. This reinforces just how much Daniel values passion and the arts, given that this value is enough to cause him to follow a stranger through town.