The funeral was originally scheduled for Friday, but has been postponed after the firefighter's widow went into labor, CFD said.
His wife gave birth Thursday to baby Evelyn Rose.
A visitation scheduled for Thursday continued as planned. The visitation was held be from 3 to 8 p.m. Thursday at St. Rita of Cascia Shrine Chapel in Chicago.
Altman's body was brought to the chapel during a procession Thursday morning.
Families, retirees and schoolchildren all lined up along 103rd Street to pay their respects to Altman.
Altman died earlier this month from injuries he suffered while battling a North Side fire.
Sheaves Slate, 27, has been charged with murder and arson in Altman's death.
Mourners were experiencing a myriad of emotions Thursday.
"In the midst of these difficult times, we hope and pray that that gift of life can give consolation, not only to the Altman family, but but to the whole city and the Chicago Fire Department," Chicago Fire Department chaplain Father Ryan Brady said. "The range of emotions must be incredible. But as I walked with her, and as we walked together, the Chicago Fire Department and her and the Altman family, it's been incredible to watch her strength, and the strength that she receives from her family."
Illinois Comptroller Susana Mendoza attended the visitation Thursday.
"It as a completely unnecessary death at the hands of a criminal, and I want to make sure the family knows I'm grateful on behalf of the city that he served," Mendoza said.
"There's not a lot of men and women willing to sign for this, where they're putting their life on the line," 36th Ward Alderman Gil Villegas said.
Public officials and many members of the Chicago Fire Department family lined up for the visitation.
Altman was a fourth-generation firefighter. His mother worked for CFD, as well.
Altman's grandfather served as fire commissioner.
The death of a father and birth of his daughter weighed heavily on all who came to pay their respects.
"It's heartbreaking, would not want to be in their situation. But I'm sure a family of firefighters, she will know her father through their stories. That's what I hope for," said Dave Gear, with the Illinois Patriot Guard.
Altman also leaves behind a 2-year-old son.
There has not been a new date set for the funeral.
Gov. JB Pritzker ordered Illinois flags fly at half-staff.