She argued, as Mr. Trump nodded along, that his company was simply “doing business” and that “there was no intent to defraud, period, the end” — speaking as though she were addressing a jury, or a television camera, rather than Justice Engoron.

Her statement, which she had not planned in advance, altered the tenor of what began as a dry proceeding, prompting squabbles between the defense team and the judge.

The substance of Mr. Trump’s defense is that his annual financial statements were merely estimates, and that valuing real estate is subjective, more art than science. The banks Mr. Trump submitted his statements to, his lawyers argued, were hardly victims: They made money from their dealings with Mr. Trump and did not rely on his estimates.

“There was no nefarious intent; it simply reflects the change in a complex, sophisticated real estate development corporation,” Mr. Trump’s lead lawyer, Christopher M. Kise, said during his opening statement. “Banks and insurers know that the statements are estimates; they are not designed to be absolutes.”

Yet Mr. Trump is starting the trial at a significant disadvantage. Justice Engoron ruled last week that the former president had persistently committed fraud, deciding that no trial was needed to determine the claim at the core of Ms. James’s lawsuit.