The Norwegian youngster - who is the son of former Leeds and Man City man Alf-Inge - scored a hat-trick during Salzburg's 6-2 win over Genk on Tuesday, becoming just the third teenage debutant to do so in competition history alongside Yakubu and Wayne Rooney.
In the Austrian side's first match in the competition since 1994, the Yorkshire-born Norway global scored his first in only the second minute before the 19-year-old completed his fourth hat-trick of the season before half-time.
Haaland, the son of former Leeds and Manchester City defender Alf-Inge Haaland, has already made his senior Norway worldwide debut and scored nine goals in an Under-20 World Cup match against Honduras in May.
His goal makes Szoboszlai only the tenth Hungarian player to score in the Champions League.
Haaland first caught the wider footballing world's attention when he scored nine goals for Norway in May when they thrashed Honduras 12-0 at the Under-20 World Cup in Poland. "Of course, he's talented, but when you combine it with his personality, that's what makes him really special".
While Bamford is now starting to prove himself, one can only wonder what would have been had the Yorkshire outfit went for Haaland instead.
Salzburg boss Jesse Marsch - who helped develop young talents such as Tyler Adams during his time in MLS with New York Red Bulls - knows he has a serious talent on his hands in Haaland.
"I'm so happy he scored three today".
"He works hard and takes nothing for granted", Marsch told UEFA.com.
Salzburg striker Erling Haaland became only the eighth player to ever score three times on their Champions League debut.
While victory at the Red Bull Arena already looks certain for the home side, more daunting tests like ahead when the forward and his side come up against both Napoli and Liverpool, also in Group E.