Police say Ms Kupfer, 24, was working alone at Croft House furniture store in Hancock Park on Thursday afternoon when a man wandered into the shop just before 2pm, attacked and killed her, and left through a back door.
Newly released video footage shows a masked man wearing a hoodie walking through an alleyway behind the store moments after the killing.
The suspect can be seen walking calmly towards Oakwood Avenue and La Brea Avenue.
LAPD detective Herman Frettlohr told reporters Ms Kupfer had been alone in the store when she was attacked, and her body was discovered by a customer 20 minutes later.
“We don’t know what the cause of the attack was, or what the motivation was yet.”
Police are urging residents and business owners in the upmarket central Los Angeles suburb to report any suspicious behaviour.
Ms Kupfer, an architectural design student from Pacific Palisades, was a graduate of the University of Miami.
Her grieving father Todd Krupfer told Fox News his daughter was a “kind soul” who was always trying to make everything around her better.
“She cared about people,” he said.
Mr Kupfer blamed political inaction for the surging crime levels in Los Angeles.
“We have a lot of politicians that somehow forgot about people and think the key to getting elected is to support the lowest rung of our society and to give them rights and somehow that’s the answer to getting votes,” he said.
“Crime is truly spiking, and we have a lot of criminals on the streets that should not be out.”
According to her Linkedin profile, Ms Kupfer had been working as a design consultant at Croft House for about a year.
She also studied at the University of Sydney in Australia in 2018 as part of a study abroad programme.
The LAPD said the suspect is a Black male of unknown age wearing a dark hoody, sunglasses, a white N-95 mask, dark skinny jeans, dark shoes. He was also carrying a dark back pack.
“Based on evidence discovered by detectives, the suspect is believed to be homeless,” the LAPD said.