Now 29, he's just graduated from the school's nursing program, ABC News reports.
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"I could barely speak English at the time when I started working at NYU," he said. "Now I reflect on it and I feel very proud of how much I accomplished."
Baez's first job at the hospital involved cleaning patient rooms, bathrooms and hallways. He was then promoted to be a patient transporter, making sure patients got where they needed to be for surgeries and tests. Being in the hospital sparked an interest in the medical field.
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"While working with the nurses, I realized I wanted to be one of them," he said. "I learned how much they advocate for their patients and the passion they have for their job."
Natalya Pasklinsky, who worked in the same unit as Baez when he was a janitor and saw him get promoted, said she always knew he had a nurse's touch.
"The way he interacted with patients, to me showed a lot of compassion," she said. "In my mind, he's a star. I think he's going to be a fantastic nurse."
Baez eventually left NYU to get his bachelor's from Hunter College, but he came right back where he started for nursing school, entering an accelerated program at NYU Rory Meyers College of Nursing.
Pasklinsky, who is now the director of simulation learning at the college of nursing, said Baez went through the program with "flying colors."
Baez's goal is to become a critical care nurse in the intensive care unit.
"Of course there were times I doubted myself," he said, "but then I felt that I wanted to do something more for myself, that I deserved better, that I wanted to continue to move forward and grow and go on with my life."