She was brought into the trauma centre of the All India Institute of Medical Sciences (AIIMS) by the police in the early hours of last Wednesday.
When I walk in to the nursery, accompanied by her paediatrician Dr Jeeva Sankar, she is awake and fixes her eyes on me.
"This is our baby," the paediatrician says. A white band on her left wrist describes her as "unknown female".
A full-term healthy baby, her tiny face is perfectly formed and it is impossible to not fall in love with her. "She is beautiful," I say.
Veena Bahri, the head nurse, laughs: "Everyone says that."
As we stand there chatting, the baby begins to bawl. She is hungry. A nurse picks her up, comforts her. She brings out a small steel cup with a long beak, fills it with milk and starts to feed her. The crying stops instantly.
With her belly full, she is calm again. Once she is put down on the bed, she rolls her left hand into a fist and sucks on her fingers. A few minutes later, she yawns. "She's going to sleep now," says Dr Jeeva Sankar.
While all the other babies in the nursery are being lovingly held by their parents, this one lies alone.
She came into the world "unwanted" and stares at an uncertain future.
"We received an anonymous call just after 01:00 informing us that a baby was lying on the pavement in Munirka district of south Delhi. The person who called us had been alerted by the baby's crying," police official Somnath Paruthi told the BBC.
When police reached the spot, they found the infant inside a plastic bag, without any clothes, distressed and crying.
The winter season is just kicking off in Delhi and in the past couple of weeks, the night temperatures have dipped.
To keep the baby warm, a woman constable wrapped her up in a piece of cloth and they rushed her to the hospital.
"When she arrived, she was somewhat cold and her blood sugar was low," said Dr Vinod Kumar Paul, who heads the neo-natal department at AIIMS.
Her medical file suggests she is now perfectly healthy. There were no signs of any external injury or abuse.
"We have given her all the mandatory vaccines and since we know nothing about her history, we are testing her for any infections or birth defects," Dr Paul says, adding that he expects to find nothing wrong with her.
"The baby's fine, she's happy, she's eating well, smiling."
In the next few days, when all her test results are in, the hospital would declare her fit to be discharged, Dr Paul said.
She would then be produced before a child welfare committee of the state government which would place her in the care of an accredited welfare home.
The committee would also order the police to try and track down her parents within a fixed time and if the parents are not found, the baby would be put up for adoption.
After her story was published in Indian newspapers, Mr Purathi says he has received at least two dozen phone calls from people wanting to adopt the baby or send her money.
He says they have registered a case "against unknown persons" and are trying to track down the parents.
"We are trying to find out from the maternity homes in the area about deliveries of baby girls," Mr Paruthi said.
It appears to be a case of abandonment, he says, adding that the parents may have other girls and may not want another daughter.
Across India, there has been a traditional preference for sons over daughters fuelled by a widely-held belief that a male child would carry forward the family name and look after the parents when they grow old while daughters would cost them dowries and leave them for their matrimonial homes.
This anti-girl bias has made female foeticide and infanticide rampant in India and it has led to a dangerously skewed sex ratio.
According to the 2011 Census, for every 1000 boys born in India, only 927 girls were born. The latest figures released at the beginning of the year show it has fallen further to 918.
Campaigners called it "genocide", saying millions of female foetuses had been aborted in recent years.
Former Prime Minister Manmohan Singh described it as a "national shame" and called for a "crusade" to save girl babies and soon after taking over in the summer of 2014, Prime Minister Narendra Modi appealed to Indians to stop killing their daughters.
Since then, he has repeated that call often - and last year, he launched a scheme asking people to save their daughters and educate them.
The messages, however, seem to be having little impact on their intended audiences.
Mr Purathi is angry: "Recently when a young woman won an Olympic medal, Indians celebrated. And now we find a baby girl being dumped on the pavement to die. We are people with such double standards."
The police, he says, have named the baby Swadha which means a "gift of God".
Dr Paul says every year, about four to six abandoned baby girls are brought into the AIIMS. I ask him if he feels upset when this happens.
"Yes, I do feel upset. It's not done, leaving a child to nature and elements. But it's God's wish. And we have to do our duty," he says.
"But then, it's also rewarding. She was left to die. She now has a second life."
An incubator in the nursery of India's premier medical institute in Delhi has been home to a tiny infant for the past few days.