SAN JOSE — When Officer Carlos Acosta approached the SUV that had been the target of a frantic five-hour manhunt in the search for a missing toddler, he peered through the window more as a father of three than a 14-year police veteran.

Moments later, he held crying 11-month-old Gabriella Quintero in his arms and breathed a sigh of relief. The little girl, who had been in the back seat of a sport utility vehicle stolen from an East San Jose driveway early Monday, was safe and sound. It was a happy ending to a kidnapping drama that riveted the Bay Area throughout the morning.

“Our mission was very direct, very straightforward: We weren’t going home without her,” said Acosta, the father of two teenage boys and 6-year-old daughter. “We all were determined to find her.”

Late Monday afternoon, San Jose police were still searching for the abductor and continued to piece together the events that led to the stolen SUV. But the most important thing had been accomplished: Little Gabriella, who had been pronounced healthy at Valley Medical Center, was reunited with her mother, Graciella Quintero.

“I can’t even imagine what she went through,” said police spokesman Sgt. Jason Dwyer of the mom. “I don’t know how you put emotions into words, not knowing if you’re ever going to see your child again.”

It remained unclear if this was a simple car theft or if the person knew the little girl was in the SUV.

“We’re not going to know what the precise motive was until we find who did this,” Dwyer added.

The ordeal began about 6:45 a.m. when Quintero placed her daughter into a car seat — without securing the straps — in a white 2006 Jeep Liberty at an Amador Court home where she rents a room. She then went back and forth, loading the idling vehicle with items, police said. As Quintero emerged from the home one final time, she saw the vehicle driving away and called 911.

San Jose police issued an Amber Alert for Quintero’s SUV and deployed several specialized teams in the search, including a police airplane and units from robbery, covert response, assault and missing persons — about 50 officers. The county’s Regional Auto Theft Task Force was also summoned. Automated calls went out to residents and businesses, and emergency alerts popped up on cellphones in the region.

Police briefly shut down a stretch of Highway 101 near Trimble Road to search for evidence.

The hours ticked away as media reports and electronic highway signs broadcast the disappearance. Then at 11:17 a.m., police got a call that the SUV had been spotted in the alleyway of an apartment complex near Andrew Hill High School. A man who saw the SUV had heard Gabriella’s cries drifting from a private driveway off Buckeye Drive in the Seven Trees neighborhood.

Because the caller had recited the license plate number to dispatchers, Acosta, a field training officer, and recruit officer Brian Simas, knew this was the sought-after vehicle before they arrived.

When Acosta pulled out the little girl from the back seat, “She did give me a hug.” He added: “She was pretty distraught, kind of lost, dazed. So I think she was happy to see us.”

Acosta accompanied the girl, just four days shy of her first birthday, in the ambulance to the hospital and watched the mother and daughter reunite.

“It was a feeling like most parents would have,” Acosta said. “She was very excited, very emotional. It was a traumatic situation that she was involved in, so she was happy to see her child happy and secure. The toddler’s reaction was kind of the same. First she started crying, then she was excited to see her mother.”

Doctors determined Gabriella was in “good” condition and released the child to her mother. Through a hospital official, Quintero — who is described as a shy woman — declined to speak to reporters gathered outside the hospital’s emergency room but made a brief statement when she returned home after 9 p.m., thanking police and everyone who “prayed for my baby.”

David Magana said Quintero rents the room in his family’s house, near Story Road and Jackson Avenue. Magana ran outside when he heard her screams as the SUV was taken. A short time earlier, he saw a woman standing near the car with bags in her hands and thought she was waiting for someone. Quintero saw something similar, but didn’t see the woman again. Dwyer said police had no further information on the woman.

“That’s all we have,” Dwyer said. “We don’t know if she’s the person who took the car. We only know the mother came out of the house and the car was gone. But that woman was the last person seen in proximity to the scene.”

But, in the end, the girl was safe.

“It’s a very rewarding day for the whole Police Department,” Acosta said. “I’m glad it worked out.”

Maria Elena Rodriguez, who lives across the street, said Amador Court is very quiet and feels safe because it is a cul-de-sac — nobody walks through who doesn’t live there.

She called Quintero “a good lady, and a devoted, dedicated mother” who may have let her judgment lapse for an instant.

“She just had one moment of blindness, just for a minute,” she said. “No one would think something like that is going to happen at that time of the morning. No souls are out.”

Anyone who might have seen the Jeep while it was traveling or has information about the case can contact San Jose robbery detectives Enrique Garcia or Jesus Mendoza at 408-277-4166, or leave a tip with Silicon Valley Crime Stoppers at 408-947-STOP (7867) or tipsubmit.org.

Eric Kurhi contributed to this report. Contact Mark Gomez at 408-920-5869. Follow him at Twitter.com/markmgomez. Contact Robert Salonga at 408-920-5002. Follow him at Twitter.com/robertsalonga.