The fictional Simpson family made their first appearance in the short "Good Night", aired in a segment of the The Tracey Ullman Show.

Simpson family
The Simpson family are the titular main characters featured in the animated television series The Simpsons. The Simpsons are a nuclear family consisting of married couple Homer and Marge and their three children, Bart, Lisa, and Maggie. They live at 742 Evergreen Terrace in the fictional town of Springfield, United States. They were created by cartoonist Matt Groening, who conceived the characters after his own family members, substituting "Bart" for his own name. The family debuted on Fox on April 19, 1987, in The Tracey Ullman Show short "Good Night" and were later spun off into their own series, which debuted on Fox in the United States on December 17, 1989, and started airing in Winter 1990.
Good Night (The Simpsons)
"Good Night" is the first of the forty-eight Simpsons shorts and the second segment of the third episode of The Tracey Ullman Show's first season. It originally aired on Fox in the United States on April 19, 1987 and was the first appearance of the Simpson family – Homer, Marge, Bart, Lisa, and Maggie – on television. After three seasons on Tracey Ullman's show, the shorts were adapted into the animated show The Simpsons. "Good Night" has since been aired on the show in the episode "The Simpsons 138th Episode Spectacular", along with several other Ullman shorts, and is one of the few shorts to ever be released on DVD, in the Season 1 DVD set.
The Tracey Ullman Show
The Tracey Ullman Show is an American television sketch comedy variety show starring Tracey Ullman. It debuted on Fox on April 5, 1987, as the network's second original primetime series, following Married... with Children, and ran for four seasons and 81 episodes until May 26, 1990. It was produced by Gracie Films in association with 20th Century Fox Television. The show blends sketch comedy with musical numbers and dance routines, choreographed by Paula Abdul, along with animated shorts. The show was conceived by executive producer, James L. Brooks. Brooks was determined to come up with a format that best suited his multitalented star. He likened the show to producing three television pilots a week.