A federal judge declared at a court hearing on Thursday that she would not let former President Donald J. Trump’s campaign for the White House affect the schedule of the criminal case in which he stands accused of plotting to overturn the 2020 election.

Hours later, the judge, Tanya S. Chutkan, fulfilled that vow by setting a schedule for the matter that moved speedily ahead and opened the possibility that prosecutors could make public more of the evidence they hope to use against Mr. Trump at trial in a court filing before Election Day.

Judge Chutkan established a series of deadlines for filings from both sides to assess the impact of several legal issues on the case, including the Supreme Court’s recent ruling granting Mr. Trump some immunity from criminal prosecution for official actions he took as president.

After an occasionally tense proceeding in Federal District Court in Washington, Judge Chutkan set a date of Sept. 26 for prosecutors in the office of the special counsel, Jack Smith, to submit an opening brief to her on the question of immunity. In that brief, prosecutors intend to set out the evidence they plan to use at trial and arguments for why none of that material — or any of the allegations in their newly revised indictment of Mr. Trump — is subject to the standards set for presidential immunity by the Supreme Court.

The brief is likely to include some evidence that goes beyond what was made public in the indictment, though portions of it could be redacted because of grand jury secrecy rules.

The hearing in Washington was held to discuss next steps in the case, which had been in limbo for nearly eight months as Mr. Trump pursued his claims to be immune from the election interference charges all the way to the Supreme Court.