Samba was one of 10 changes Enzo Maresca made to the side that won a dramatic derby against Manchester United with 10 men on Sunday, and the 17-year-old made his case for more minutes going forward.
"To get a debut like that is mind-blowing. I couldn't believe it myself," said Samba, the son of former Blackburn and QPR defender Chris Samba.
"But that's just the beginning, I've got a big career ahead of me. It was a great debut."
Brazilian Allan Elias also struck on his first outing since a £34 million move from Palmeiras, while Rayan Cherki slotted home City's second in characteristically cool fashion.
Norwich also made nine changes with their focus on trying to achieve promotion from the Championship and were completely outclassed even by City's second string.
Samba made sure his debut was one to remember as he stooped to head in Allan's cross after Daniel Grimshaw flapped at a cross.
Ayyoub Bouaddi was given his first Etihad start following a 100 million euro arrival from Lille and marked it with an assist for Cherki to race clear and steer beyond the onrushing Grimshaw.
Amid City's major moves for Bouaddi, Enzo Fernandez, Elliott Anderson and Iliman Ndiaye, Allan's signing was largely overlooked.
But he showed his potential with a fine individual jinking run and finish to fire into the far corner on 48 minutes.
Just moments later, Samba made the most of some more slack Norwich defending to curl brilliantly into the far corner.
Another of City's talented crop of teenagers rounded off the scoring when Ryan McAidoo stroked in late on.
Victory extended Maresca's perfect start as Pep Guardiola's successor at City to six consecutive wins across three competitions.
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