The 21-year-old academy product struck at the death to seal a 2-1 win over Brighton on Sunday.
And now he wants to carry on playing a prominent role under Nuno Espirito Santo, having waited patiently for an opportunity since returning from a loan spell at Swansea in January.
“I felt good coming back from Swansea. Me and the manager, when he called me back, we had good confidence in each other,” said Gibbs-White.
“He’s been hard on me, and I know I’ve got to be patient. I feel like every time I’ve sort of had an impact on a game. I’ve done alright.
“It’s about staying patient and when you get the chance, you take that chance.
“I’m looking to progress as a player and I want to stay here. I’ve been here since I was a little kid and my dream is to play for this club.
“Chances keep coming and I feel like I’m performing well, maturing well, physically getting stronger and starting to read the game better.”
Gibbs-White curled the ball home in the 90th minute against the Seagulls – minutes after somehow missing from point-blank range after being teed up by Adama Traore.
On reacting to the miss and getting off the mark, he said: “I’m still speechless now.
“It’s what I dreamed of as a kid. It’s an unbelievable feeling. It’s about time.
“After I missed the first one, I was devastated. But I kept my composure and took my chance when I got the second one.”
Gibbs-White added: “Each day is a stepping stone, still trying to impress and I’d love to stay here. I feel ready, fit and stronger than ever.
“My experience going out on loan – even though it was short – and the manager having confidence with me to bring me back, I feel like I have progressed as a player.”