The fourth criminal case involving Donald J. Trump is likely to come to a head next week, with the district attorney in Atlanta expected to take the findings from her election interference investigation to a grand jury.

The Georgia investigation may be the most expansive legal challenge yet to the efforts that Mr. Trump and his advisers undertook to keep him in power after he lost the 2020 election. Nearly 20 people are known to have been told that they could face charges as a result of the investigation, which Fani T. Willis, the district attorney in Fulton County, Ga., has pursued for two and a half years.

Ms. Willis has signaled that she would seek indictments from a grand jury in the first half of August. In a letter to local officials in May, she laid out plans for most of her staff to work remotely during the first three weeks of August amid heightened security concerns. Security barriers were recently erected in front of the downtown Atlanta courthouse, and at lunchtime on Tuesday, 16 law enforcement vehicles were parked around the perimeter.

On Tuesday afternoon, two witnesses who received subpoenas to appear before the Fulton County grand jury said in interviews that they had not received notices instructing them to testify within the next 48 hours, a sign that the case will not get to the jury until next week.

Earlier this month, Mr. Trump was indicted in a federal case brought by the special counsel Jack Smith, in an investigation also related to election interference that listed a number of unindicted co-conspirators. The Georgia inquiry, elements of which overlap with the federal case, involves not just the former president, but an array of his aides and advisers at the time of the 2020 election, several of whom are expected to face charges.

If Mr. Trump were to be convicted in a federal prosecution, he could theoretically pardon himself if he were re-elected president. But presidents do not hold such sway in state matters. Moreover, Georgia law makes pardons possible only five years after the completion of a sentence. Getting a sentence commuted requires the approval of a state panel.

Mr. Trump’s lawyers have described an indictment in Georgia as a foregone conclusion in recent legal filings, and the forewoman of a special grand jury that heard evidence for several months last year strongly hinted afterward that the group, which served in an advisory capacity, had recommended Mr. Trump for indictment.

Two grand juries have been hearing cases at the Fulton County Courthouse during the current Superior Court term, which began on July 11 and runs through Sept. 1. Twelve of 23 jurors need to agree that there is probable cause to hand down criminal charges after hearing evidence in a case.

“The work is accomplished,” Ms. Willis recently told a local TV station. “We’ve been working for two and a half years. We’re ready to go.”

Her office began investigating in February 2021 whether the former president and his allies illegally meddled in the 2020 election in Georgia, which Mr. Trump narrowly lost to President Biden.

The inquiry focused on five things that happened in Georgia in the weeks after the election. They include calls that Mr. Trump made to pressure local officials, including a Jan. 2, 2021, call to Georgia’s secretary of state, Brad Raffensperger, during which Mr. Trump said he wanted to “find” nearly 12,000 votes, or enough to reverse his loss.

Ms. Willis’s office also scrutinized a plan by Trump allies to create a slate of bogus electors for Mr. Trump in Georgia, even though Mr. Biden’s victory had been certified several times by the state’s Republican leadership. The office also investigated harassment of local election workers by Trump supporters, as well as lies about ballot fraud that were advanced by Rudolph W. Giuliani, Mr. Trump’s personal lawyer at the time, and other allies during legislative hearings after the election.

At times the investigation stretched beyond Fulton County, including to rural Coffee County, about 200 miles southeast of Atlanta, where Trump allies and contractors working on their behalf breached the election system in the first week of 2021.

Ms. Willis has said that by bringing charges under Georgia’s version of the Racketeer Influenced and Corrupt Organizations Act, her inquiry could cover a wide range of issues. Broadly speaking, so-called RICO laws require prosecutors to prove that a group of people conspired to take part in organized criminal activity.

With RICO indictments, Ms. Willis said in an interview last year, “there are sometimes acts that occurred outside of the jurisdiction that are overt acts that we can use if they are evidence of the greater scheme.”

The special grand jury heard evidence in the case for roughly seven months and recommended more than a dozen people for indictments, its forewoman has said. The Trump aides and allies whose conduct has been scrutinized in the inquiry include Mr. Giuliani, who was told last year that he was a target who could face charges. A number of other lawyers who worked to keep Mr. Trump in power have also been under scrutiny in the investigation, including John Eastman, Sidney Powell, Jenna Ellis and Kenneth Chesebro.

Mark Meadows, the former White House chief of staff, was ordered to testify before the special grand jury last year. He traveled to Georgia after the election and became personally involved in the efforts to keep Mr. Trump in office despite his loss.

Ms. Willis’s office also sought the testimony of Jeffrey Clark, a former high-ranking official at the Justice Department, but was blocked by the department. Mr. Clark sought to intervene in Georgia on Mr. Trump’s behalf after the 2020 election, over the strong objections of more senior officials at the department.

More than half of the 16 Republicans who were bogus Trump electors in Georgia are cooperating with Ms. Willis’s office, but others have been told they could face charges, including David Shafer, the former leader of the state Republican Party.

Mr. Trump’s lawyers have called the Atlanta inquiry a “clown show” and have filed numerous court motions seeking to disqualify the district attorney and derail the investigation. They argued that the special grand jury proceedings were unconstitutional, and that Ms. Willis has made prejudicial public statements.

But Georgia judges have shown no inclination to act before any charges are brought. Both the presiding Fulton Superior Court judge, Robert C.I. McBurney, and the Georgia Supreme Court have rejected motions from the Trump team in recent weeks.

Two witnesses who have been subpoenaed to appear before Fulton grand jurors currently hearing cases — George Chidi, an independent journalist, and Jen Jordan, a former state senator — said Tuesday afternoon that they had not received 48-hour notices to appear this week. Mr. Chidi was one of a handful of reporters who discovered a December 2020 meeting of bogus Trump electors, and Ms. Jordan, a Democrat, attended a legislative hearing in which Mr. Giuliani and other Trump allies advanced false claims of election fraud.

This has been a busy year for Mr. Trump’s lawyers. In April, he was indicted in state court in Manhattan on 34 felony counts related to his role in what prosecutors described as a hush-money scheme, covering up a potential sex scandal to clear his path to the presidency in 2016.

In June, he was indicted in Miami on federal criminal charges related to his handling of classified documents and whether he obstructed the government’s efforts to recover them after he left office.

Christian Boone contributed reporting.