In the days of absolute monarchy, the king would start his day whenever he felt like. Those who wanted to get something from him would come as early as they could in order to be available whenever he called. Haman actually expected to have to wait until the king had gotten up, dressed, eaten and officially opened the court. Once the king woke up and had the records read to him, he did not think about how early it was or how inconvenient it might be to call in his advisors. He knew that someone was on duty at all times in case he wanted something (as was shown by having the royal records read to him).
And the king said, "Who is in the court?" And Haman had come to the
outside court of the king's house, to petition the king to hang
Mordecai on the gallows that he had prepared for him.
Note that the king did not pay any attention to Haman and what he might want or what emergency might have arisen to bring him to the court. As soon as he entered the king started.
And Haman entered, and the king said to him, "What should be done to a
man whom the king wishes to honor?" And Haman said to himself, "Whom
would the king wish to honor more than me?"