Gordon insists the transfer represents not a destination but a starting point for what he expects to achieve at the highest level.
Gordon made the comments to talkSPORT after coming on as a half-time substitute in England's 1-0 World Cup warm-up victory over New Zealand in Tampa, in which Harry Kane scored the only goal just before the interval.
"It's been a bit of a whirlwind of two weeks, but the best two weeks I've ever had for me and my family. I've told them from a very young age, I said in my interview, that I would get to this point. I'm not satisfied at all to just play for Barcelona. I want to win everything. This is where my career begins in my mind."
The 25-year-old had not featured competitively since April 12 — a Crystal Palace match — having been an unused substitute for Newcastle United's final four games of the season as his departure became increasingly certain. He acknowledged the rustiness but said his fitness was encouraging.
"Even when you have two days off football, you feel like you never played a game. It's crazy. You lose your touch, you lose everything.
"I was fitter than I thought in that game. I'm on track really, really well. It's difficult because the pitch was dry, so even getting your touch right was tough."
On the battle with Marcus Rashford for a starting berth in England's World Cup opener against Croatia on June 17 — Tuchel handed Rashford the number 11 shirt and Gordon number 18 — the forward was dismissive of the significance.
"I couldn't care less. I think if you go through this team, you could put any player 1-11. We're all good enough. I'm here to win for England. I don't care about me individually."