The family of Marlen Ochoa-Lopez said at a news conference the baby -- named Yovani Lopez after his father -- has recently been able to breathe without the help of a machine.
"It's still a long way to go for the baby, but the baby is fighting and surviving," Frank Avila, an attorney for Marlen's husband, told reporters.
Yovani's mother was brutally murdered in April when she was lured to a home on the Southwest Side and strangled with a coaxial cable.
Clarisa Figueroa, 46, and her 24-year-old daughter Desiree face first-degree murder charges in the death of the 19-year-old, who had gone to the women's home in response to a Facebook offer of free baby clothes, according to Chicago police. The older woman’s boyfriend, 40-year-old Piotr Bobak, is charged with concealing a death by homicide, police said.
Officials originally said the child was in grave condition, and not expected to survive.
Family friend Julie Contreras said Friday that doctors and hospital staff have been providing the best care for the baby and asked the public to keep praying for the child, WLS-TV reported.
The family's lawyer said Friday although they're thrilled about the news of Yovani having breathed on his own. The family, however, still has concerns about why one of the women who was arrested for the murder of Ochoa-Lopez was able to pretend the baby was hers for so long, according to FOX32.
The Illinois Department of Public Health has opened an investigation into Advocate Christ Medical Center in Oak Lawn, where the infant was brought on April 23 by Clarisa Figueroa.
The hospital's handling the case has raised questions, since the Chicago Police Department and the state's Department of Children and Family Services both said that staff at the hospital did not alert them after determining that Figueroa had not just given birth to the gravely ill newborn.
The 19-year-old's body was found dumped in the garbage behind the Figueroas’ home on May 15, roughly three weeks after she was reported missing.
The hospital has declined to say whether or when it contacted authorities when it learned that Figueroa was not the baby's mother, citing state and federal regulations.
Fox News' Frank Miles, Louis Casiano and The Associated Press contributed to this report.