The narrative of Single Papa unfolds with Gaurav Gehlot, a young man, concluding his divorce proceedings with his wife, Aparna, in the first episode. Gaurav pleads with the judge that his desire for children contrads Aparna's unwillingness to have them. Aparna counters by asserting that Gaurav is not equipped to be a responsible parent. The debate escalates, and Aparna urges the judge to finalize the divorce as a compromise is unattainable.

Six months later, Gaurav returns from his morning jog, perplexed by the odd comments from neighbors in his colony. At home, his sister, Namrata, reveals that their parents have placed a matrimonial advertisement for him in the local newspaper. Gaurav is agitated and reiterates his sole objective is to have a child, not to find a partner.
That night, Gaurav joins his friend Pawan at a club, who encourages him to pursue a connection. In an attempt to restart his life, Gaurav approaches Inaara and they hit it off, only to be interrupted when they discover a baby in the backseat of Gaurav's car. Inaara panics and attempts to flee, but Gaurav receives a call from Namrata informing him that their father, Jatin, is missing. The situation deteriorates when Inaara confides that she is married and does not want her husband to discover her infidelity.
Later that night, Gaurav brings his intoxicated father home from a friend's house. His mother, Poonam, engages in an argument with Jatin, with Namrata occasionally intervening. To everyone's surprise, Gaurav brings the baby into the house and explains he found the infant in his car. Together with their househelp, Reshma, the family deliberates on their next steps. They struggle to feed, clean, and settle the baby for sleep. Gaurav decides to alert the authorities in the morning and takes the baby to his room, filled with a sense of responsibility and uncertainty about what lies ahead.
In the quiet hours of the night, a piercing cry pierced the stillness, and the baby's lips turned a hushed blue. Panic-stricken, Gaurav sprang into action, rushing the infant to the hospital. Doctors revealed that the child required immediate heart surgery, a news that set Gaurav's heart racing. He paid for the procedure, which was a success, though the baby remained under observation.
As the family gathered at Goldie's abode to discuss wedding plans, a disagreement over jewelry stirred up tension. Gaurav tried to diffuse the situation with a playful jest, but the mood turned sour. Just as things seemed at their tensest, the police arrived, accusing Gaurav of abandoning his child and whisking him away for a paternity test. The news left Goldie's family in shock.
At the hospital, Gaurav's story was interrupted by Romila Nehra, who introduced herself as the Chairperson of the Central Authority of Child Adoption (CACA). She accused Gaurav of deliberately abandoning his child. The paternity test confirmed his innocence, and a heated argument ensued. Gaurav threatened to sue Romila for defamation.
Later that day, Goldie apologized to Namrata for his parents' behavior. The next day, Gaurav returned to the hospital only to learn that the baby had been moved to an orphanage. There, he met Shlok, a boy whose parents ran the place. Shlok introduced Gaurav to the baby, and Gaurav's expression was one of profound emotion. When asked to suggest a name, Gaurav recommended Amul, explaining that he had found the baby in an Amul carton in his car.
Over the next few days, Gaurav realized how deeply he missed the baby and decided to adopt him. Back at the orphanage, Shlok explained how challenging adoption was for a single man in India and introduced Gaurav to his mother—Romila once again. The two argued yet again.
The episode ended with Romila vowing never to let Gaurav adopt Amul, while Gaurav swore to keep trying with determination in his heart.