Jesse Pulkkinen was born in Laukaa, Finland. According to his own words, PUlkkinen started playing ice hockey at Team LKP's skating school when he was around five-six years old. He transferred to JYP as a D-Junior.
In June of 2023, Pulkkinen signed a 2+1-year SM league contract with JYP. He started teh 2023-2024 season with the club's U20 team, where Pulkkinen scored 11 goals and 17 assists in 18 games. He led JYP in goals by a defenseman. After the season, Pulkkinen signed a three-year contract extension with JYP, through the 2026-2027 season.