Pre-debut vignettes are specifically this trope, producing a character for the audience to get a feel for, before they even wrestle a match.
For example, Razor Ramon's 1st promo showed his disdain for intellectuals and that all he respects is strength. Meanwhile, he'd "live the good life" while showing nothing but disdain for ex-girlfriends and wait staff.
Spiritual Successor Carlito had pre-debut vignettes that saw him walking around the Caribbean, smugly lecturing the audience on what "cool" is... then taking a bite of his apple and spitting in someone's face.
Carlito: I spit in the face of people who don't want to be cool!
Val Venis' pre-debut vignettes showed him lounging around porn movie sets clad in only a towel, spewing out Double Entendres like it was going out of style. One such vignette ended with the not-at-all-subtle tagline "Val Venis Is Coming." Another featured a cameo by Jenna Jameson, the It Girl of late 90s porn.
Fitness guru Simon Dean debuted with an informercial for his "patented Simon System." You could even call the number at the bottom of the screen!
Probably the mother of 'em all as far as pre-debut vignettes go was Mr. Perfect, in which he'd perform incredible athletic feats, and brag about being the perfect athlete. In one, he bowled a perfect game. In another, he'd throw a football, then run downfield and catch his own throw.
Chris Jericho's WWE debut is one of the most famous instances of this trope ever. He interrupts a promo by The Rock - The Rock!! - to proclaim himself as "saving" the company.
The debut of Kharma (the former Awesome Kong) in WWE. While the vignettes that had been airing painted her as no one to be trifled with, her first actual appearance came at Extreme Rules 2011, where she came out after Michelle McCool lost a Loser Leaves Town match. She took her time getting to the ring and stalked an absolutely terrified McCool (a multiple time Women's/Diva's champion, mind you) for a good two minutes before getting in the ring and completely destroying her with an Implant Buster, then cackled insanely while the rest of the WWE Divas division looked on in horror from the locker room, knowing they are monumentally screwed.
"Stone Cold" Steve Austin when he became King of the Ring 1996 "You sit there and you thump your Bible, and you say your prayers, and it didn't get you anywhere! Talk about your psalms, talk about John 3:16...Austin 3:16 says I just whipped your ass!"
When he first became Stone Cold, he refused to wrestle a jobber and lost by forfeit. Then he came back and beat up the guy anyway.
John Cena debuted in 2002 as a generic wrestler wearing generic gear coming to the ring to generic music so bland the audience likely tuned it out. But the impression of a lifelong midcarder or one destined to be future endeavored vanished when he took the fight to Kurt Angle, countering Angle's finishing slam and ankle lock during their match and in general showing the attitude of a man who would never back down to any threat.
Six months into Cena's WWE career, he was on the road to being lost in the shuffle until a Halloween episode of Smackdown, where he appeared dressed as Vanilla Ice, cutting promos in freestyle rap. He hasn't looked back since.
When Tommy Dreamer started out in ECW, he was a hated pretty boy wrestler who looked like a WCW reject. Then, he had his famous Singapore Cane match with the Sandman, which he lost and, as part of the stipulation, had to be caned. With his back bloodied and him being unable to stand, Tommy should've stayed down. Instead, he got up and demanded, "Thank you, sir! May I have another?!" He got his wish, and it was here that Tommy went from a hated pretty boy to the "heart and soul" of ECW.