Upon college graduation, Dr. Delgado worked as the Children's Talent Coordinator for the popular television show Sesame Street, where she was responsible for selecting and casting the children who appeared on the show. While finishing her PhD, she joined the U.S. Department of Health and Human Services as a Senior Policy Analyst, where she helped address health concerns across the U.S., including environmental health issues in Puerto Rico (1979-1983). She then joined the Immediate Office of the Secretary in 1983, became the Special Assistant on Minority Affairs, and served as a Member of the Coordinating Committee for the Secretary's Task Force on Black and Minority Health. The report produced by this Task Force, also known as the Heckler Report, was the first effort of the U.S. government to document what was known about the health of racial and ethnic communities.

In 1985, Dr. Delgado was selected as President and CEO of the Coalition of Spanish-Speaking Mental Health Organization, becoming the first Hispanic woman to hold the role. She expanded its mission with the organization and launched the first environmental health program in 1988. The organization is now the National Alliance for Hispanic Health and continues its leadership on clean air and clean water as essential to health. Her responsibilities include serving on boards, overseeing research, administering budget and financial operations, advancing health policy, education, and public speaking. In addition to her role at the Alliance, Dr. Delgado serves on the Board of Governors for Argonne National Labs, Lovelace Biomedical Research Institute, and the U.S. Soccer Foundation. For her knowledge and expertise, the HHS Secretary appointed her to the National Biodefense Science Board. Dr. Delgado has received many awards, including a Doctor of Letters by the Board of Trustees of the State University of New York, the highest recognition offered by SUNY, and was named among the 101 Most Influential Latinos in the U.S. in 2018 by Latino Leaders. Dr. Delgado is also a three-time recipient of the Dr. Harvey Wiley Award from the Food and Drug Administration, among several other awards and honors, for her work advancing healthcare equity. She is the author of The Buena Salud Guide to Understanding Depression and Enjoying Life with a Foreword by Rosalynn Carter, which received critical acclaim and other books and articles.

Among their career highlights, she mentions the "wonderful and smart people who continue to toil with [her]." These people include all those throughout the Alliance family who are advocates for Hispanics and the best health for all.