A federal judge in Florida will hold a hearing on Friday to pick a new date for former President Donald J. Trump’s trial on charges of mishandling classified documents, a move that is likely to have major consequences for his legal and political future.

The judge, Aileen M. Cannon, has already said she is inclined to make some “reasonable adjustments” to the timing of the trial, which for the moment, at least, is set to start on May 20 in Federal District Court in Fort Pierce, Fla. Several decisions Judge Cannon has reached in recent months about the pacing of the case have made it all but impossible for the trial to start as scheduled.

What remains to be seen is just how long of a delay Judge Cannon ends up imposing.

On Thursday evening, Mr. Trump’s lawyers and prosecutors in the office of the special counsel, Jack Smith, sent Judge Cannon their proposals about when the trial should begin.

Mr. Smith’s legal team, hewing to its long-held position of trying to conduct the trial before Election Day, requested a date of July 8. But after months of seeking to delay the trial until next year, Mr. Trump’s lawyers suddenly reversed themselves and suggested a date of Aug. 12.

The hearing in front of Judge Cannon, who was appointed to the bench by Mr. Trump in his waning days in office, is being held just days after a decision by the Supreme Court that increased the possibility that the former president might not face trial before Election Day in his other federal case — the one in which he stands accused of plotting to overturn the 2020 election.

The justices agreed to decide whether Mr. Trump is immune from prosecution on the election interference charges, scheduling arguments for the end of April and keeping the proceedings in the trial court frozen until they resolve the issue. As a practical matter, the Supreme Court’s decision to take up the case meant that the election trial was unlikely to begin before September, in the heat of the general election campaign.