Currently in his rookie campaign, Albon joined Toro Rosso for the start of 2019, having left Formula 2 to race in Formula E for Nissan e.Dams.
The Thai-Britsh driver admits that he is in an "incredible" situation, as he has found himself at the seat of a race-winning car in such a short space of time.
"It is quite laughable, when I look back at it, just having the announcement," Albon said on Thursday.
"I called my mum and dad, it's a journey that we've all took from 2012. I don't think my career has been very fluid. I've had a few ups and downs.
"To be in this position is incredible. There are a lot of drivers who have done amazing jobs in Formula 1, and have never been in a championship-winning team. It's a big opportunity for me and I really know that."
Albon is set to take a hefty engine penalty this weekend at Spa-Francorchamps, as he is being fitted with the 'Spec 4' Honda engine.
The 23-year-old will start Sunday's race from the back of the grid, and although he admitted it relieves some pressure, Albon says he would have liked to have given qualifying a shot.
"We'll just go into the weekend more focused on race-pace which of course means more laps as well," he said. "That will be the target and I think that feeling going into qualifying, it'll be a different atmosphere.
"But I still would have liked to have given it a go and see how I would have done in qualifying, trying to start further up than what I will be."
Bahrain International Circuit - Winter testing