Three years ago, a 16-year-old Bianca Andreescu wrote herself a fake cheque.

That cheque was a mock-up of the one given to the US Open champion.

Now, after beating the great Serena Williams 6-3 7-5 in Saturday's compelling final, the composed Canadian is ready to cash a real one worth about £3.1m.

"I've been dreaming of this moment for the longest time," the 19-year-old said of winning her first Grand Slam title, wiping away tears as the magnitude of what she had just achieved finally hit.

"For it to become a reality is crazy."

Crazy is a word which Andreescu, like most teenagers, readily uses to describe unexpected situations and one which has cropped up regularly in her chats with the media over the past few days.

Not without good reason.

Twelve months ago and struggling with injury, she lost in the first round of qualifying at Flushing Meadows and was ranked outside of the top 200 in the world.

But she has become one of the most talked-about young players on the planet following a remarkable rise this year.

Andreescu, whose Romanian parents Nicu and Maria emigrated to Canada in the 1990s, had only played six tour-level matches at the turn of the year.

Since then she has won prestigious WTA Premier titles at Indian Wells and Toronto, rising to 15th in the world as a result and raking in £1.79m of her £1.97m career prize money.

Now the gains are even higher after becoming a Grand Slam champion: she will climb to fifth in the world, take home a winning prize of £3.13m and, surely, become a face recognised by many outside of the parameters of Canada and tennis.

"I never really thought about being famous. I'm not complaining though," she smiled.

"My goals have been to just win as many Grand Slams as possible, become number one in the world. But the idea of fame never really crossed my mind.

"It's been a crazy ride this year. I can definitely get used to this feeling."

And the prize money? "Don't ask me that because I have no clue. I've never held that much money in my life!"

Succumbing to the trappings of fame and wealth at a young age looks unlikely for the warm teenager, who has been nurtured by father Nicu, an engineer, and mother Maria, a chief compliance officer for a finance firm.

Maria herself has become a popular figure, particularly among social media users, thanks to her striking look, bold fashion statements and as she brings Coco, Andreescu's pet dog, to sit on her lap during matches.

Andreescu, an only child, describes her as "the coolest person I know and my role model".

She also has her mum to thank for helping develop the mental resilience which she needed to block out a passionate home crowd at Flushing Meadows as Williams threatened to derail her hopes.

"I started meditating and visualising ever since I was 12 or 13 when my mum introduced it to me, and I know it wasn't such a big thing back then, but now it's getting more popular because I think if you can control your mind, then you can control a lot of things," she said.

"I think that's what's been working really well for me. I just kept doing that.

"When I'm on the court in front of these big stages, I'm really good at just blocking everything and staying in the zone."

Belief is not something Andreescu has in short supply, illustrated by the way she struts around the court - even on the cavernous Arthur Ashe Stadium, even in her first Grand Slam final - with her head always up.

And that confidence exudes in a marvellous all-round game which has the variety to pull opponents apart, as well as having a killer forehand already rated as one of the best in the game.

Williams, the 23-time Grand Slam champion rated as the greatest female player ever, could not cope with the teenager's consistent depth as she was hustled out of a record-equalling major.

"I feel like Bianca plays well under pressure. She goes out and she plays hard," the 37-year-old said.

"She does what she does best, and that's move up to the ball, that's hit winners, that's play with a ton of intensity."

Andreescu had already earned six wins over top-10 players this year - Caroline Wozniacki, Elina Svitolina, Angelique Kerber (twice), Kiki Bertens and Karolina Pliskova - going into Saturday's final.

And Williams, who she led against in their Rogers Cup final in Toronto last month before the American retired with a back injury, became the latest victim.

This run to the US Open title means Andreescu has won 14 straight matches and an extraordinary 45 of her 49 matches this season.

She is the first teenager to lift a Grand Slam singles title since Maria Sharapova won the 2006 US Open aged 19 and matched Monica Seles' record of winning a major in the Open era on only her fourth appearance in a Grand Slam main draw.

While Andreescu's rise has been rapid, a dream-like year has also not been without its challenges.

She missed a large chunk of the season after suffering a shoulder injury at the Miami Open in March which, after an ill-judged attempt to play the French Open, forced her to miss the entire grass-court swing, making her swift ascent and formidable winning record even more remarkable.

"It's definitely a process of life. You're never going to have ups all the time," she said.

"So I think in those moments, you just have to deal with it the best that you can, which is to just keep fighting for your dreams and just stay as persistent and persevere as much as you can.

"I know in those moments you feel like you can't.

"But if you believe that there are good times ahead, then those tough moments are definitely worth it. I think it builds you as a character.

"I think everyone should go through it because it just makes you stronger."