A young Brooklyn mother pushing her baby in a stroller Thursday did what all New Yorkers do when the elevator doors open — she walked in.

But the car was stuck between floors below them and the two tumbled onto its roof, with the mom’s weight crushing her infant daughter to death.

The tragic accident happened at about 11:45 a.m. on the 23rd floor of 3415 Neptune Ave. — a Coney Island high-rise riddled with violations, including 45 directly related to the elevators.

Aber Al-Rahabi, 21, told investigators that she didn’t notice that the elevator car wasn’t there when the doors opened — and just pushed 6-week-old Areej Ali into the open space, police sources said.

The two fell several feet onto the roof of the car stuck between the 22nd and 23rd floors of the building — part of the Bay Park apartment complex.

Al-Rahabi landed on top of her daughter.

The impact killed the baby and sent the elevator plummeting down to the 17th floor, where first responders pulled them both out.

Areej was pronounced dead a short time later at Coney Island Hospital.

Salah Ali, 70, the infant’s grandfather, said the mother is in “bad shape.”

“She’s in the hospital. She’s injured,” Ali told reporters at the scene. “[It] breaks my heart. That was my grandchild.”

Al-Rahabi is still in the emergency room at Coney Island Hospital recovering from the accident.

A neighbor said that when Areej’s father came home, he nearly passed out. “They’re all screaming and crying next door,” the neighbor added.

Jeff Delacruz, who lives in the building, said his aunt spoke to the baby’s mother. “She keeps saying, ‘Everything is OK. It’s OK. God only gave me my baby for one month . . . She’s probably traumatized,” said Delacruz, 28.

His wife said the elevators are always out of service.

“About a week ago, the same one was out of service. The door just didn’t open,” said Elizabeth Delacruz, 26.

The Bay Park complex has a “chronic problem” with its elevators, according to one of hundreds of Department of Buildings complaints.

There’s one active complaint from Sept. 30 about the elevator that caused Areej’s death.

Two complaints for that elevator from July 17 that have been resolved and a complaint from March 9, 2015, that says the elevator is “constantly getting out of service” and “has not been working for 2½ weeks.”

There are 45 total elevator complaints dating back to 2000 at 3415 Neptune Ave. There are also 159 elevator-related violations in the complex dating back to 1994 — with 31 still active.

The Department of Buildings said the elevator involved was last inspected on Aug. 8, and one nonhazardous violation was issued because the emergency phone in the car didn’t work.

But DOB inspectors determined it could “safely remain in operation.”

They added the elevator passed inspections in January 2016, including a thorough, “once-every-five-years inspection” where special load tests are conducted to measure the weight limits of the car.

The Starrett Corporation, which owns the building, issued a statement saying: “We are saddened by today’s tragic incident . . . The incident is now under active investigation and we are cooperating fully with all authorities and agencies to determine the facts surrounding the event. We extend our deepest sympathies to the families involved and management is making arrangements to offer grief counseling upon request.”