Who was considered as the first cosplayer ever? Or, who popularized cosplaying anime? Was cosplaying started in Japan as well or it started elsewhere?
The Costume Fandom: All Dressed Up with Some Place to Go! written by By Dr. John L. Flynn says that it goes as far back as:
At the First World Science Fiction Convention in New York in 1939, a 22-year-old Forrest J Ackerman and his friend Myrtle R. Jones appeared in the first SF costumes among the 185 attendees. The future editor of Famous Monsters of Filmland was dressed as a rugged looking star pilot, and his female companion was adorned in a gown recreated from the classic 1933 film Things to Come. Both of them created quite a stir among the somber gathering of writers, artists and fen plural of fan), and injected a fanciful, imaginary quality into the convention's overly serious nature.
According to the Cosplay wikipedia page,
The term was coined by Nobuyuki Takahashi of the Japanese studio Studio Hard while attending the 1984 Los Angeles Science Fiction Worldcon. He was impressed by the hall and the costumed fans and reported on both in Japanese science fiction magazines.
However, the act of "cosplaying" was around before the term was coined by Nov Takahashi:
It is said that the first cos-play ever performed at a fan event in Japan was that of a young woman portraying Tezuka Osamu's character Umi no Toriton (Triton of the Sea) back in 1978. But contrary to popular belief this performance seems to have taken place not at the Comic Market but at the "Ashicon" science fiction convention, and was performed by none other than the then 20-year-old Kotani Mari, now renowned as a critic and author of science fiction.
With this as an additional source(Japanese).