Baumgartner is charged with three counts of murder and one count of attempted murder in the shooting at the HUB Mall on campus.
A directed indictment in the case was filed with Alberta Court of Queen's Bench on Tuesday.
That means the Crown seeks to skip a preliminary hearing, which determines if there is enough evidence to go to trial.
Instead, the case would proceed directly to trial.
"Anything that saves dragging on a painful process is good news," said Peter Ernst, the father of Michelle Shegelski, one of the guards. "I am happy that it’s proceeding."
Family members of Eddie Rejano also expressed relief the trial will be held sooner rather than later.
Baumgartner was one of five G4S security guards who were making a cash delivery to an ATM at the HUB Mall on campus June 15.
The 21-year-old is accused of shooting the other four guards, killing three of them, and fleeing with the money.
He was arrested the next day trying to enter the United States at a border crossing in B.C.
Baumgartner will appear in court on Sept. 7 for a trial date to be set.
Last week, friends and family of Brian Ilesic, one of the guards killed in the shooting, held a fundraiser to provide money for the man’s 12-year-old daughter.
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