The 20-year-old had a dream Man City debut in the Champions League as he scored in the 3-2 win over Red Star Belgrade.
He put City ahead after just 19 minutes, while playing in a hostile atmosphere in Serbia.
Hamilton later won a penalty, that Kalvin Phillips would go on to convert.
He has has been with the club since he was nine and Guardiola was reminded of a moment that happened six years ago.
Back in 2017, the City boss put his arm around a ball boy to deliver instructions.
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Even though his side beat Crystal Palace 5-0, it showed his meticulious detail. He wanted the ball boy's to get the ball back in play faster.
Following that victory over Red Star Belgrade, he was asked about that moment in 2017.
"I didn't know it," he said.
He was then shown a picture and he said: "Oh wow, he grew up. Look at that."
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Guardiola added: "What a goal and what a game.
"I'm so happy for him. He's training often with us and we saw his skills one against one. He scored a fantastic goal and made a penalty."
Hamilton himself admitted it was a surreal moment to be scoring on his debut.
"The manager has given us the opportunity in training and in the game. Playing with the best players, you always improve," said Hamilton.
"He put me on the right wing, something different for me. I'd not really played there. I saw it as a challenge and I took it and I enjoyed every moment.
"It's definitely just the start and [I want] to kick on from here."