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I did some research, and here’s the scoop we were looking for:

Snuffleupagus – A large shaggy brown elephant-like creature that debuted in 1971 on the children’s program SESAME STREET/PBS/1969+. For many years adults on Sesame Street believed that Aloysius Snuffleupagus was the imaginary friend of Big Bird. In 1985, however, Snuffleupagus was seen by everybody for the first time. Snuffleupagus also had a sister named Alice who debuted in 1987.

Now we know.