It was about 2:30 on Monday afternoon when the first 96 potential jurors filed into a drab courtroom in Lower Manhattan to encounter the world’s most famous defendant: Donald J. Trump.

Some craned their necks to catch a glimpse, an indication of the undeniable power of Mr. Trump’s celebrity.

But not long after, more than 50 of those same prospective jurors — drawn from one of the nation’s most liberal counties — were dismissed because they said they could not be impartial about the 45th president.

The beginning of the first criminal trial of a former American president drew intense security, loud demonstrations and smothering media coverage to a dingy Lower Manhattan courthouse that will be the unlikely center of American politics for the next six weeks.

And if the first day is any indication, the trial may well be a surreal experience, juxtaposing the case’s mundane-sounding criminal charges — falsifying business records — against the potentially seismic effect it could have on the presidential race.