Jury selection began in the Manhattan criminal case, but many who might weigh Donald J. Trump’s fate told a judge that they could not be impartial.

But the ritual of choosing the jury got off to a slow start as more than half of the first group of 96 potential jurors raised their hands to say they could not be fair to Mr. Trump, demonstrating the challenges of picking an impartial panel in a city where the defendant is widely loathed. The judge immediately excused them.