CNN — At Thursday’s hearing in the federal election subversion case against Donald Trump – the first proceeding before Judge Tanya Chutkan since the Supreme Court granted him some immunity in the prosecution – the trial judge did not finalize a schedule for the next steps in the case, but previewed her thinking on how the case should advance.

She was skeptical of the Trump team’s request that she first decide whether the then-Vice President Mike Pence-related allegations in the indictment were immune, and Chutkan repeatedly stressed the discretion she believes she has for how she structures the proceedings in her courtroom.

Though Thursday’s one-hour-and-15-minute hearing was mainly about process, a sharp back-and-forth she had with a Trump attorney brought attention to how the 2024 election is looming over the case.

Here are takeaways from the hearing:

Chutkan will lay out next steps as soon as Thursday

The judge did not issue a ruling from the bench but said she planned to put forward a scheduling order as soon as possible, which she said could be later Thursday.

That could lay out the steps in the case that will play out before the November election.

During Thursday’s hearing, prosecutors explained why they want the chance to file an opening brief that would argue why they believe their new indictment complies with the Supreme Court’s immunity ruling. Trump’s attorneys argued against that and proposed a longer schedule.

Chutkan pushed prosecutor Thomas Windom for dates on how quickly the special counsel’s office could file the brief they proposed defending the new indictment.

Windom deferred to the judge – not putting on the record a date itself – while telling the judge they would need two to three weeks, meaning the end of this month.

“We do actually have to write this thing,” Windom said, prompting Chutkan to joke that maybe Windom had it in his binder.

“I would be surprised by that,” Windom responded.

At the same time, he emphasized that prosecutors would leave the exact timing “to the court’s discretion.”

In the brief, Windom said prosecutors “would set forth for the court” why the conduct is “private in nature and not subject to immunity.”

Election looms over hearing, but Chutkan says she’s not considering it

As the judge debated with Trump attorney John Lauro over how quickly she should move to allow the prosecution to file a brief defending their indictment on immunity, they eventually addressed the political elephant in the courtroom: the looming presidential election.

After a back and forth with the judge over what the process should be for deciding the immunity issues in the case, Lauro acknowledged that among his team’s concerns about the prosecutors’ proposed approach is what would be aired on the court’s public record at a “sensitive time.”

The crux of the process disagreement comes down to who gets to file their immunity brief first and when that brief gets filed.

“This court is not concerned with the electoral schedule,” Chutkan pushed back.

“We are talking about the presidency of the United States,” Lauro said.

“I am not talking about the presidency,” Chutkan said. “I am talking about a four-count indictment.”

“The subtext of your argument here about these sensitive times … it strikes me that what you’re trying to do is affect the presentation of this case so as not to impinge on an election,” she added.

Lauro denied that his arguments were connected to the presidential campaign.

“The decisions here will not just affect this case, it will affect the republic going forward,” Lauro said.

Trump has repeatedly complained that the new indictment filed last week was an attempt to interfere with the campaign – just as he complained about his New York trial in the spring – but Chutkan’s comments signaled she isn’t going to wait until after November 5 before moving forward on the issues that have to be dealt with in the case following the Supreme Court’s immunity decision.

‘Exercise in futility’ to set a trial date

At the end of Thursday’s hearing, Chutkan acknowledged the elephant in the room: There were still too many issues to resolve to set a trial date in the case.

“It’s sort of an exercise in futility at this point,” she said, noting that whatever decision she makes on immunity will be appealed, which means the trial will pause once again while the appellate process plays out.

Both Trump’s lawyers and prosecutors agreed that it was too soon to set a trial date.

Chutkan does plan to issue an order with the next steps in the case to get the immunity issue moving, she said, and it could come as soon as later Thursday.

Of course, it’s not just the appeals process that makes a future trial so murky. If Trump wins the 2024 election, he is poised to toss out the special counsel and the case against him altogether once he returns to office.

A chilly reception for Trump’s claims about teeing up the Pence conduct first

Chutkan did not seem particularly convinced that, when deciding the immunity issues in the case, she should deal specifically with the Pence-related claims first.

Trump’s attorneys made the aggressive argument, first laid out in their filings late last week, that the whole case must fall if Trump’s interactions with his vice president are deemed immune from prosecution.

In Thursday’s hearing, Lauro was particularly focused on that argument and tried to persuade the judge that dealing with the Pence conduct as a standalone issue would be a more efficient way of doing things.

He contended that it would save the court from doing lengthy briefings on other the allegations in the indictment if she decides the whole case must be dismissed on the Pence issue alone. He also insisted that the Supreme Court viewed a finding that the Pence conduct was immune as fatal to the indictment, a claim Chutkan shot down.

“The ruling is clear, crystal clear,” Lauro said, prompting a chuckle from Chutkan.

Chutkan swipes at Florida judge’s ruling dismissing classified documents case

Chutkan hinted that she was dubious of Trump’s coming attempt to get the DC case dismissed on the grounds that special counsel Jack Smith was supposedly illegally appointed, even as Chutkan has said she’d let the former president file that motion to dismiss.

She took a swipe at the ruling that Judge Aileen Cannon handed down this summer dismissing the classified documents case on that basis, calling that ruling not particularly “persuasive.”

She also emphasized that a concurrence by Justice Clarence Thomas – which Cannon’s ruling cited – that laid out those constitutional concerns was “dicta,” meaning non-binding language. And she noted that there is already DC Circuit precedent on the books upholding the constitutionality of special counsels, which would be binding on her as a trial judge in Washington, DC.

Nevertheless, she is letting the Trump team take a shot. However, when his lawyers file the motion that asks for permission to formally make those arguments, they must elaborate on why they should be allowed to do so, Chutkan said.

This story has been updated with new developments.

CNN’s Hannah Rabinowitz and Holmes Lybrand contributed to this report.