Shortly after coming to the outside world, Diana interrupted a terrorist attack and was named "Wonder Woman" by the press. She continued to use her gifts to fight for peace and justice in Man's World. She later fought who she thought to be Ares, though in truth it was Phobos and Deimos who were disguised as their father. Fearing that she would eventually discover the truth and free Ares from his prison beneath Themyscira, the Gods of Olympus sent Phobos and Deimos to erase all memory of Themyscira from Diana's mind. The twin gods were unable to erase the memory, so instead they later implanted false memories regarding her home to deceive Diana, leading to a completely separate origin story and causing her to hallucinate new adventures. Diana was unaware that her memories had been tampered with, and believed the falsifications until her search for the truth led her to Ares himself years later.
The JLA's first trip to the universe is where Owlman is found hacking computer systems to get the info he needs. There, the JLA fights recruits the Crime Syndicate of America has recruited. Their second trip was when Batman followed Superwoman, and defeats her. After taking out Superwoman, he calls the JLA, and alongside the JLA travels to the moon, to get to the Crime Syndicate's headquarters. From there on, every JLA'er fights against their counterparts, and Wonder Woman manages to even win against her counterpart, Superwoman.