Now the Australian is adamant he can do it again - and this time the world will be watching as he seeks to dethrone the Wimbledon champion, maybe on Centre Court, in the match of his life.
The last time they met in 2020, Alcaraz was just 17, already being touted as the sport's next big thing - correctly, as it turned out - and Vukic, seven years his senior, got the better of the "phenom" in three sets in a French Open qualifier, saving a match point on the way.
Of course, "Carlitos'' was just a "child" then, accepts Vukic, and not the man who's gone on to achieve "insane" feats in the game at just 21, with three grand slam singles titles already under his belt.
But a win's a win. Vukic knows others won't give him, as the world No.69, a cat in hell's chance in the second-round clash on Wednesday (Thursday morning AEST), especially after he only scraped through with a topsy-turvy 6-7 (9-11) 6-4 6-4 3-6 7-6 (10-8) win over Sebastian Ofner.
Yet asked if he felt he could beat Alcaraz, Vukic exclaimed: "Oh, definitely.
"Everyone's beatable, everyone's human. If things go my way, if I play well, serve well or if he doesn't have his best day - hundred per cent I can win.
Defending Wimbledon champion Carlos Alcaraz looked impressive in his first-round win. (AP PHOTO)
"The more I'm playing these guys, the more you realise they're playing the same sport. Obviously, they're the best at the sport, but they can also sometimes not play well.
"Who knows? Sometimes you wake up and have low energy. Or what if his girlfriend's pissed him off or something like that the day before? Things happen and you need to try to capitalise."
Since that win, Alexei Popyrin, Alex de Minaur (twice), Thanasi Kokkinakis, Jordan Thompson and Max Purcell have all tried but failed to beat Alcaraz.
Over that time, Vukic has watched the Spaniard turn into a sunny, charming acquaintance on tour and evolve into a great player, but what impresses him most about Alcaraz is his demeanour in the most searing of spotlights.
Practising with him during a tournament in Beijing last year, what Vukic found most striking was the incredible level of attention the youngster has to live with.
"I'm just on court and no one knows who I am, and he comes on and everyone's going insane,'' Vukic said.
"I'm just like, 'This guy lives in another world'.
"I probably wouldn't want that, to be honest. But it comes with the territory, right? If I were ever in that position, even though I probably wouldn't want it now, I'd have to embrace it.
"And that's what he does very well. He embraces it. He's always smiling, so kudos to him and how he behaves and how he does it.
"When we played in Paris he was a child, but there was so much hype around him. You could tell he had a raw power to him already there, but back then I wasn't thinking, 'Oh, this guy's going to be No.1 in 12 to 18 months'. It was insane, his rise.
"Him and (Jannik) Sinner are going to be the dominant forces in the game. He'll be there for a long time.
"But when he steps out on court, if he's not ready to win, then I'm going to try to do my best to take it from him."
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