According to the interviewee, Sadat's cameraman who videotaped his original speech where he said he would go to Israel, the process started a number of years earlier.
An Israeli woman, Ruth Liss, wrote a letter to Anwar Sadat's wife Jihan after the 1973 war. As People magazine wrote in 1980:
After the 1973 Yom Kippur War Jihan received a letter from an Israeli mother, Ruth Liss, whose frogman son had been killed placing explosives in an Egyptian harbor. The woman appealed to Mrs. Sadat "as a woman and a mother" to help find her son's body. "Believe me, I was crying," Jihan recalls. "The letter was so human. I too have a son." Impulsively, she asked the minister of defense to search for the body (it was never recovered)—and wrote back to Liss without consulting her husband. "All my friends advised me not to do it," she recalls. "They said I could not write to the enemy and that I would harm my husband politically." Later, after the letter was mailed via France, she told Sadat. He reprimanded her and subsequently, on learning she had answered another letter from an Israeli student, Anwar grumped, "You are making trouble for me."According to the interview, up until then Israelis were not recognized in Egyptian society except as caricatures, of Golda Meir's big nose and Moshe Dayan's eyepatch.
In the podcast, the interviewee says that Sadat was furious when Jihan told him she wrote to an Israeli, asking how dare she write to the enemy, but then he saw that the Israeli media were very appreciative towards Jihan's letter. He told his wife that he had never seen such a warm reaction from the Israeli people. "I want to reach the Israeli people as much as you did in two sentences," he is reported to have said.
So part of the impetus for Sadat's gamble may have been from how Israeli society embraced his wife's contact with a grieving Israeli mother.