The vehicle had apparently collided with water infrastructure on the roadside, and the vehicle overturned. Williams drove near the scene and parked, and people had already gathered near the vehicle to help. Someone suggested flipping the vehicle right side up again.
Williams said the driver was screaming, "Do not push the van over."
"And the guy's like, 'I think there's a baby in there,' " Williams said. "And when you look through the windshield, you can see that she's sitting in glass, holding glass, so she has cuts."
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The driver also was reaching out to support the baby, who was in a car seat, to keep her from falling onto glass, Williams said.
"And that's when you realize, like, we need to help her as soon as possible," Williams said. "Like, this is not a wait-for-the-paramedics thing."
Williams climbed onto the vehicle with the help of another person to try to reach the woman and the baby from the passenger's side, which was facing the sky.
As the rescue unfolded, Mitzi Connell called 911 and started recording with her phone.
"He was amazing. I mean, without question he just leaped up there," Connell said.
As he reached into the vehicle, Williams reassured the woman that he wasn't going to let the baby fall, he said. He unhooked the seatbelt from the car seat, pulled the baby out and handed the child to someone.
During the rescue, the vehicle was smoking. The driver tried to pull glass out of her hands, but Williams encouraged her to focus on him and get out.
"I said, you know, it's pretty serious. There's smoke coming from your car. It's not a good idea. And she gives me her hand, and then I pull her up. And as I pull her up, you can tell she's in a lot of pain," he said.
After police and paramedics arrived, the woman and the child were taken to Flagler Hospital. When Williams asked if she was OK, she nodded, he said.
When he knew everyone was safe, Williams shared what happened with his supervisor and finished up his route. Connell shared the story and videos with UPS.
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"I'm glad there are people like him in the world," Connell said.
Williams said he hasn't heard any updates about the driver or the baby. A condition update was not available from authorities.
"I wish I did. If I could find out I would definitely, you know, send her a get-well card and just make sure she's good," he said. "I mean, she did give me the thumbs up."
Williams said he has been with UPS for three years but has never dealt with a situation like that before. He said he didn't think twice about helping.
"I'm just glad I was at the right place at the right time," Williams said.
Follow Sheldon Gardner on Twitter: @sheldonrgardner