Then in November, Gonzalez broke his silence, telling a newspaper reporter a gruesome story: He stabbed the boy to death, dismembered him in the bathtub, put his remains in plastic grocery bags and dumped them in trash bins around the city.
The account baffled prosecutors, police and Gonzalez's lawyer — all of whom have said there was no evidence found in his apartment to corroborate his story.
The alleged confession also stunned Gonzalez's ex-girlfriend, Daisy Colon, who had spent more than three agonizing months pleading for word of her son.
"It's lies," Colon said recently. "Why would you deny having your son, then, after all this time, why would you come out and say something like that? He wants the attention. He wants people to stop looking for Giovanni, and that's not going to happen."
Police and prosecutors in this Boston suburb declined repeated requests for comment from The Associated Press. They have not said publicly whether they believe Gonzalez's account, whether they think the child is dead or alive, or why the father would have confessed to such a deed. The 36-year-old meatpacker has not been charged with killing his son.
In the interview with The Boston Globe, Gonzalez said that during a visit to his apartment Aug. 15-17, his son misbehaved by spitting, throwing bottles, ripping a bedsheet and jabbing him in the back with a pen.
On Sunday, the day Giovanni was supposed to go back to his mother, Gonzalez said, the boy was yelling when Gonzalez picked up a kitchen knife and stabbed the child.
"It happened fast," he told the Globe. "I was upset. It happened in a moment."
Gonzalez told the reporter he loved his son and regretted killing him.
Gonzalez's lawyer, Lawrence McGuire, said no evidence taken during police searches of Gonzalez's apartment backs up his story. "I would say the district attorney is skeptical," McGuire told The Daily Item of Lynn. McGuire did not return calls from the AP.
Some forensic experts said Gonzalez could have killed and dismembered his son the way he described, then used bleach or another strong cleaning agent to remove the blood. But others said it is highly unlikely he could have killed his son in such a ghastly way without leaving any trace.
"If someone shed blood and they cleaned it up, you can still find it," said Gary Rini, a former police officer and crime-scene investigator who is now a consultant in Cleveland. "The only way you are not going to find it is if they remove the surface upon which the blood was shed — period." In this case, that would require removing the kitchen floor and the bathtub.
Steve O'Connell, a spokesman for the district attorney, would not say what kind of testing police did for blood in Gonzalez's apartment or whether any new tests were done after Gonzalez gave his account from jail, where he was being held on child endangerment charges.
Two weeks after Gonzalez's alleged confession, he was charged with parental kidnapping and misleading police. The misleading-police charge was based not on what he told the reporter, but on his initial insistence that he had not seen his son the weekend he disappeared.
Colon said she and Gonzalez lived together until Giovanni was 2. She said she ended their relationship after Gonzalez swung a chair at her, hitting a cabinet behind her. While they were together, Gonzalez helped take care of Giovanni and never hurt him, she said.
After the couple split up, Gonzalez petitioned a court for visitation rights, and the boy began spending weekends last summer with his father.
After the first two visits, Giovanni chattered happily about how he and his father had gone to the park, colored and watched movies together, his mother said.
On Friday, Aug. 15, Colon dropped Giovanni off again. Witnesses said they saw the boy on Saturday, kicking a ball with his father, then accompanying his father to an appointment with a therapist. But when Colon went to pick up Giovanni on Sunday afternoon, no one answered the door. The next day, police arrested Gonzalez.
Police found blood on a mop in the apartment and said Gonzalez had a cut and bandaged finger he would not explain. But authorities later said the blood was the father's, not his son's.
Colon pleaded for Giovanni's safe return on television and on the Internet. The National Center for Missing & Exploited Children put up thousands of posters. The case was also featured on "America's Most Wanted."
The 33-year-old mother said she firmly believes her son is still alive and thinks someone is helping Gonzalez hide him, maybe to punish her for ending their relationship.
"Whoever has him, just leave him at the police station or leave him somewhere where he can just say his name," Colon said. "I don't even need to know who it is. I just want my son back."