Inosuke was raised by boars for most of his life before the Final Selection; it was revealed later that he was born into a family with an abusive father and caring mother. Eventually, Inosuke's mother, Kotoha, and he fled from their family.
Afterwards, Inosuke—who was still an infant at the time—and his mother were taken in by Doma into his Eternal Paradise cult. Kotoha loved to sing to Inosuke but would apparently change the song lyrics each time. However, after finding out that Doma eats his worshippers, Kotoha fled with her son. Running aimlessly for a human village, Kotoha eventually ended up at the top of a cliff. Seeing no escape route, Kotoha makes a last ditch effort to save Inosuke by dropping him into the river below the cliff. It was after this that Inosuke was taken in by boars and his mother was devoured by Doma.
While Inosuke participated in the Final Selection at Mt. Fujikasane, he was off-screen for all of this arc. His presence is only hinted by Oyakata, when a crow tells him the results of the selection. [chapter 8, page 20]
Inosuke had wandered into the Kyogai's Drum house presumably looking for demons to kill in order to become stronger, but due to the nature of Kyogai's blood demon arts, ended up trapped for 3 days. He first appears when Zenitsu and Shoici are searching for an exit, having been separated from Tanjiro and Teruko. Zenitsu slides open a door which he believed was the exit, and desperately opens another when the first door fails. Behind that door is Inosuke, who immediately hurtles out and knocks down another door before running down the opened corridor. Zenitsu is left shakened, with Shoichi wordlessly judging him. TBC