The stage for Esther’s pitch is set in Chapter 4 of the Megilla named for her. That’s when she learns, through Mordechai, of Haman’s plan of genocide for all the Jews in Achasuerus’ (or Xerxes’, if you’re nasty) domain. She’d like to petition the king to change his mind but, as she tells Mordechai, “any man or woman who goes to the king’s inner court without permission–there’s just one rule–they die.” It’s pretty clear her pitch is a risky one.
Esther goes anyway. After 3 days of fasting and market research (we can only assume), she enters the king’s inner court. Without permission. Achasuerus points his golden scepter at Esther, signifying he won’t kill her. Esther invites her husband and Haman to a string of parties, the second of which is her pitch meeting. When she finally pitches, in chapter 7, Esther demonstrates an intimate knowledge of her audience and the market context.