The nine-month-old underwent surgery after suffering burns to his face and chest following what police described as a "cowardly" and random attack in a Brisbane park.
Police on Wednesday appealed for help to identify the alleged attacker, releasing footage of a man running away from the park after the "terrifying" incident.
The baby was with family and friends at Hanlon Park, Stones Corner, at midday on Tuesday when a man approached, police said.
The mother said "some guy" came up behind them and poured a coffee all over her son's head.
"My baby boy doesn't deserve this, no one does," the mother posted on social media.
"I wish he poured the hot coffee all over me and not my boy."
A woman organising a GoFundMe page for the baby said she was the friend who was with the mother during the alleged attack.
"My friend and I were sitting in Hanlon Park ... with our two babies when a strange man came up behind her nine-month-old son and poured a thermos of boiling hot coffee over his little body and then fled!" she wrote.
"This was a callous, random attack on my friend's baby. He does not deserve this pain and suffering."
The boy remains in a stable condition in a Brisbane hospital.
"It's torture. I am supposed to be his protector and I couldn't protect him," the mother told Nine Network on Wednesday night.
"I'm just having flashbacks all the time about what happened."
The mother said a nurse who lived nearby heard the baby's screams and ran over to help, taking them to her apartment to shower the boy before an ambulance arrived soon afterwards.
The woman says she was in a park in Brisbane with her son when he was attacked. (Darren England/AAP PHOTOS)
She said her friend ran after the alleged attacker but he got away.
Police described it as a deliberate and unprovoked attack.
"It is callous and cowardly," Detective Inspector Paul Dalton told reporters on Wednesday.
"Going to a park on a beautiful winter's day in Brisbane, enjoying your time ... to be attacked like this and approached like this, it must be terrifying.
"In 35 years of being a police officer I've never come across a job where a child this young in these circumstances has been attacked."
Police on Wednesday released CCTV footage of a man running from the park and down the street.
They said finding the man was critical to their investigation.
The man was wearing a black hat, glasses, a shirt and shorts and is believed to be aged around 30 to 40 with a proportionate build and tanned skin.
Anyone with information is urged to contact police.
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