He needed only 15 minutes on the field as a substitute to open his account. Now the flying Finn hopes he can maintain that meteoric rise towards making an instant impact in Europe for the Hoops.
The striker's signing from Schalke came at the very end of the transfer window, and he had to immediately jet off to join his Finnish national team-mates for their World Cup qualifiers.
Pukki only got to Lennoxtown at the end of last week, but manager Neil Lennon felt he was ready to take a place on the sub's bench at Tynecastle on Saturday.
He marked his debut for the club with a headed goal, the culmination of an impressive cameo in which he showed agility, ability, quick feet and the intelligence to link up the play.
Pukki's goal four minutes from time was the icing on the cake, and the 23-year-old - who first impressed Schalke with his performances for HJK Helsinki against the Bundesliga side - is eager to get involved when the Hoops play AC Milan in the San Siro on Wednesday.
He knows how tough a test it will be for Lennon's Bhoys in Italy, but said: "I've only been here a few days, so I don't know everyone.
"But I think we have a very good squad and a good chance.
"It's not an easy group, but, of course, we believe in ourselves and we're looking to go through.
"Last year, I played with Schalke in the Champions League, but not as a starting player. So I'm hoping to play a lot of games in the competition."
Pukki appreciates he could not have had made a better start to life as a Celt, and was blown away by the reception he received from the Hoops fans at Tynecastle.
His aim is to repay everyone involved in making him so welcome - in the best way possible.
He said: "I hope to score a lot of goals."