Mr. Cohen has concluded that his life has been utterly destroyed by his relationship with Mr. Trump and his own actions, and to begin anew he needed to speed up the legal process by quickly confessing his crimes and serving any sentence he receives, according to his friends and associates, and analysis of documents in the case.

He has told friends that he is mystified that he is taking the fall for actions he carried out on behalf of Mr. Trump, who remains unscathed. Still, he is resigned to accepting responsibility.

“He realizes that he needs to move on with his life, and that he’d like to begin that process as soon as possible,” said Andrew W. Albstein, a lawyer and friend who wrote a letter of support on Mr. Cohen’s behalf to the judge.