At first Gloria sang only on weekends, because she was still attending the University of Miami. A year and a half after Gloria joined the group, by then renamed the Miami Sound Machine, the band recorded its first album for a local label. Renacer was a collection of disco pop and original ballads sung in Spanish.

Although Estefan was somewhat plump and very shy when she joined the band, she slimmed down with a rigorous exercise program and worked to overcome her natural reticence.