The former X Factor UK judge was shown in the first hour of the Fox reality singing competition's series premiere. Cole was permanently replaced by Nicole Scherzinger after the Los Angeles auditions.
Cole was impressed by the first contestant, 13-year-old Rachel Crow, saying: "You had me before you even sang, and then when you sang, I was like, 'Oh my God, we've found ourselves a little star!'"
She also had praise for 42-year-old single mother Stacy Francis, telling her: "I was completely and utterly blown away with every single word you sang, and I could feel the whole room was willing you to win... and you just won. You're amazing."
> 'The X Factor' USA premiere launch: Show One - Live Blog
> 'The X Factor' USA: What are the critics saying?
Cole was also seen rebuking auditionee Miranda Singleton - who said that she wanted to be "the next Madonna" - when she argued with Simon Cowell following negative comments from the music mogul.
The Girls Aloud singer told the 30-year-old: "You have a really bad attitude."
Cole's appearance was warmly received by The New York Times, whose review said: "In the premiere [Cole] just kind of disappears mid show, without much explanation, and suddenly Nicole Scherzinger of Pussycat Dolls is in her chair.
"It's a downgrade. Ms Cole showed glimmers of being interesting; in two seasons as a judge on The Sing-Off on NBC, Ms Scherzinger was a pretty face but, judicially speaking, not much more than a seat warmer."
> X Factor USA premiere screening: What the judges said
The Chicago Tribune said that Scherzinger was not "an obvious improvement" at the judges' table, while the Los Angeles Times complemented Cole's "fabulous Geordie accent".
However, The Sun's US editor Pete Samson wrote: "Cheryl appears in most of the first show and holds her own - but it's hard to deny her replacement, Pussycat Doll Nicole Scherzinger, immediately looks more comfortable in the American arena."
A supposed X Factor USA production insider told The Mirror: "They tried to make Cheryl come across as a smiling dummy, but it has backfired and people love her.
"Simon is not going to be happy with the initial reviews because Nicole is being knocked and Cheryl has only praise. Maybe he made a bad call which could affect the success of the show long-term."
> X Factor USA reveals episode schedule, live finale dates
Sunday Mirror celebrity columnist Dean Piper tweeted: "Loving reading the reactions on twitter as the #XFactorUSA airs in the States. Our Cheryl is great on it! Do we agree West Coast?"
Meanwhile, Ben Grossman, editor-in-chief of television trade magazine Broadcasting & Cable, wrote: "Cheryl Cole will end up a TV star in America, it's just a matter of time. If I'm (sic) an agent or exec, I'd be finding a vehicle for her now."
The X Factor USA continues on Thursday at 8/7c on Fox, while the series premiere will be shown in the UK on Thursday at 8pm on ITV2.
> X Factor USA: Four new preview videos
Watch X Factor USA hopeful Chris Rene's audition below: