Answer by taking a quote from the following article:

Gloria Estefan (nee Fajardo; born September 1, 1957) is a Cuban-American singer, songwriter, actress, and businesswoman. She started off her career as the lead singer in the group called "Miami Latin Boys" which was eventually known as Miami Sound Machine. Estefan's breakthrough success with "Conga" in 1985 made her known worldwide. The song became Estefan's signature song and led to the Miami Sound Machine winning the grand prix in the 15th annual Tokyo Music Festival in 1986.

Starting in 1977, Miami Sound Machine began recording and releasing various albums and 45s on the Audiofon Records label in Miami. The first album from 1977 was entitled Live Again/Renacer and was released with two different covers. After several more releases on the Audiofon label as well as the RCA Victor label and Miami Sound Machine's own label MSM Records, the band was signed to Discos CBS International and released several albums, 45s, and 12"s beginning with the 1978 self-titled album Miami Sound Machine. Growing in popularity in both the U.S. and around the world, the group would continue recording and issuing various works for Discos CBS International through 1985. In 1984, Miami Sound Machine released their first Epic/Columbia album, Eyes of Innocence, which contained the dance hit "Dr. Beat" as well as the ballad "I Need Your Love". Their more successful follow-up album Primitive Love was released in 1985 launching three Top 10 hits on the Billboard Hot 100: "Conga" (U.S. No. 10), "Words Get in the Way" (U.S. No. 5), and "Bad Boy" (U.S. No. 8), as well as "Falling in Love (Uh-Oh)" (U.S. No. 25) which became follow up hits in the U.S. and around the world. "Words Get in the Way" reached No. 1 on the US Hot Adult Contemporary Tracks chart, establishing that the group could perform pop ballads as successfully as dance tunes. The song "Hot Summer Nights" was also released that year and was part of the film Top Gun. Their next album, 1987's Let It Loose, went multi-platinum, with three million copies sold in the US alone. It featured the following hits: "Anything for You" (No. 1 Hot 100), "1-2-3" (No. 3 Hot 100), "Betcha Say That" (No. 36 Hot 100), "Rhythm Is Gonna Get You" (No. 5 Hot 100), and "Can't Stay Away from You" (No. 6 Hot 100). "Can't Stay Away From You", "Anything for You", and "1-2-3" were all No. 1 Adult Contemporary hits as well. In that same year, Estefan took top billing and the band's name changed to Gloria Estefan and Miami Sound Machine. In 1989, the group's name was dropped, and Estefan has been credited as a solo artist ever since. In 1988, after the worldwide chart success of single "Anything for You", her Let it Loose album was repackaged as Anything for You.

What was she up to in the mid 1970s?
Starting in 1977, Miami Sound Machine began recording and releasing various albums and 45s on the Audiofon Records label in Miami.