The victim, aged 26, suffered fatal injuries in the attack at a bus stop in west Croydon, south London.
Police said he became involved in an argument with a second man that led to the fatal knife attack.
Detective Chief Inspector Cliff Lyons, who is leading the investigation, said the circumstances of the murder are "particularly tragic".
He said: "This was a shocking attack in a public place in the early evening.
"The victim's three year-old daughter was with him when he was attacked, though fortunately she wasn't physically injured.
"Even more tragically, his partner had given birth to a son just that morning.
"The investigation is at a very early stage and I'm keeping an open mind about the circumstances of the attack at this point.
"A number of witnesses have already come forward but I believe there are still people with information we need to speak to and I urge those people to get in touch.
"In particular, we need to talk to two teenage boys who were at the bus stop when the incident happened who may have significant information.
"They are described as black, aged between 15 and 20 years old, of slim build and wearing hooded tops."
Emergency services were called to London Road, west Croydon, shortly after 6.15pm last night.
The victim, who was black, was taken to Mayday Hospital where he was pronounced dead less than an hour later.
A Sure Start shop, a Government-run centre for children and parents, remained closed today and was cordoned off by police.
Witnesses at an office opposite the scene said the man might have picked up the girl from the daycare centre.
A Metropolitan Police spokesman said several bystanders dialled 999 after the seriously injured man was found in the street.
He said: "We believe we know the identity of the deceased but await formal identification and confirmation that all next of kin have been informed."
A 22-year-old man arrested on suspicion of murder remains in custody at a south London police station.
The attack took place close to a bus stop outside a Lidl supermarket, a short distance from West Croydon railway station.
Police were still at the scene today as two areas of pavement alongside London Road remained cordoned off.
A white forensic tent erected over the bus stop, which is used by buses travelling towards Thornton Heath, was taken down this morning.
Blue-suited forensics officers were examining the area around the bus stop for evidence. They took samples from the bus timetable as well as the shelter.
The short stretch of London Road, which was reopened to traffic, is mainly specialist ethnic supermarkets, halal butchers and new-build flats.
Several residents at flats overlooking the scene said they were unaware of the stabbing until police arrived doing door-to-door inquiries last night.
One resident, who did not wish to be named, said: "We had real trouble getting home last night but we didn't know why until the police came knocking on the door."
Another resident said they were shocked: "You don't expect it to happen on your doorstep."
Staff at the Fitness First leisure centre overlooking the scene said they heard about the incident but said the victim had not been visiting the gym.
Workers in a nearby ethnic food supermarket said many shops were shut at the time of the incident.
They only discovered what had happened when they arrived for work this morning to see the police cordon.
A London Ambulance Service spokesman said: "We were called just after 6.10pm last night to reports of a stabbing in London Road in Croydon.
"We sent one single response car and one ambulance crew to the scene. An adult male was taken to hospital as a priority."
Detective Chief Inspector Cliff Lyons said police were still looking for two black youths aged between 15 and 20 who they know were in the area at the time.
He would not confirm whether they were being sought as witnesses or suspects, but said: "They were wearing hooded tops and were of skinny build.
"It's obviously crucial we discover who they are, and where they are."
He said the incident was "shocking".
"A 30-year-old man was at this bus stop with his daughter, aged just three years, and then an incident occurred where this man was stabbed in front of his daughter, and he died in front of her eyes.
"That is shocking and bad enough, but during the course of this investigation police have discovered that he was visiting his newborn son, born that very day.
"It is a double tragedy for the three-year-old, his wife and the son he will never see."
Mr Lyons said officers were still trying to find out if the man had seen his newborn son before he died.
He said London Road, where the incident occurred, is "one of the busiest roads in the area", and "people must have seen something".
He said he hoped that the tragic circumstances, which had left him and his team "quite upset", would "prick people's consciences to make people pick up the phone and call us".
He said police were keeping an open mind about the motive behind the attack, but added that, as yet, the issue of gang activity "had not come up".
He said officers had found a number of knives in the area and were also reviewing CCTV footage from a number of cameras, but he would not say if the murder weapon had yet been found, or if the attack had been caught on CCTV.
He added: "I cannot at this moment rule out a random attack."
Mr Lyons said police were still establishing the man's background, but confirmed that he was local to the area.
He said 80 to 100 police staff, including 50 detectives, were currently working on the case.
A post-mortem examination was being carried out on the man.
The man was treated at the hospital where his partner had just given birth, said Mr Lyons.
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